ABSTRACT
Abstract
Methods for improving the prediction accuracy for an ensemble machine learning model are described. In some instances, the methods comprise: (i) receiving data characterizing levels of trust in one or more machine learning models that form the ensemble machine learning model; (ii) calculating a prediction error estimate for each of the one or more machine learning models based on a trust score for that machine learning model and relative weights calculated for the data points in a training data set used to train that machine learning model; (iii) calculating a normalized weight for each of the one or more machine learning models using the prediction error estimate calculated for each; and (iv) adjusting an output prediction equation for the ensemble machine learning model, where the adjustment is based, at least in part, on the normalized weights calculated in for each of the one or more machine learning models.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the priority of U.S. Provisional Application No. 63/228,379, filed Aug. 2, 2021, the entire contents of which are incorporated herein by reference.
FIELD
The present disclosure relates generally to methods for detecting and countering adversarial attacks on machine learning models, and more specifically to methods for incorporating a model trust score when training an ensemble machine learning model.
BACKGROUND
Machine learning (ML) has been adopted across many facets of modern society, with applications ranging from face recognition algorithms used to suggest who to tag in a photo on social media platforms to deep learning algorithms that help with medical diagnoses. While there are a plethora of potential benefits that may be derived from the growing range of ML applications, the increased reliance on ML does not come without risks.
ML algorithms often require vast amounts of data and computational resources to train the machine learning model for a particular application. In order to help alleviate some of the costs associated with data collection and computational resources, publicly available datasets and pre-trained models can be used. While using publicly available datasets and pre-trained models help reduce costs and time, they also come with additional risks. Pre-trained models may be based on data that is not publicly available and/or the source code may not be available to protect intellectual property. This makes it difficult to verify that the model will behave in the expected manner when deployed operationally. If a dataset is large, it can be infeasible to ensure that the dataset is clean and complete. It is known that noisy data, contaminated data, incomplete data, or inherent biases in the data can affect the performance of a machine learning system.
In addition to these non-malicious concerns about machine learning model performance, there are also a growing number of vulnerabilities where an adversary can directly or indirectly attack a ML system such that it affects the system's decision-making outcome. These attacks can be based on the model architecture of the system, the data the system is trained on, or a combination of both. All of these issues lead to concerns about the trustworthiness and accuracy of the machine learning models created.
Ensemble-based machine learning is a common approach that is used to improve accuracy and confidence in ML-based decisions. Ensemble based machine learning is the process of combining multiple models to apply decision-level fusion which can increase the likelihood of making accurate decisions. By using ensemble classifiers, for example, algorithms that are highly accurate but only partially trusted can be incorporated into the ensemble to improve the overall prediction accuracy of the system. Given the primary focus of improved accuracy, little attention has historically been paid to the notion of trust relative to the classifiers incorporated in an ensemble model. Indeed, only a few studies exist that examine the notion of trust for single classifier approaches. Thus, there remains a need to develop methods for incorporating a trust factor in developing and training ensemble machine learning models, and for detecting adversarial attacks that impact the accuracy of the model's predictions.
SUMMARY
Accordingly, disclosed herein are methods for incorporating a trust factor in developing and training ensemble machine learning models, thereby improving the prediction accuracy of the ensemble model, and for detecting adversarial attacks that impact the accuracy of the model's predictions.
Disclosed herein are methods for calculating a prediction error estimate for a machine learning model comprising: receiving data characterizing a level of trust associated with the machine learning model; training the machine learning model on a training data set to determine relative weights for data points in the training data set; and using the data characterizing the level of trust and the relative weights for at least a subset of the data points in the training data set to calculate a prediction error estimate for the machine learning model, wherein the prediction error estimate increases with a decreasing level of trust.
In some embodiments, the data characterizing the level of trust in the machine learning model comprises a trust score. In some embodiments, the trust score is a real number having a value ranging from 0.0 to 1.0. In some embodiments, the trust score is calculated from the received data. In some embodiments, the received data comprises data relating to a sensitivity of model predictions to input data quality, a sensitivity of model predictions to distributional shifts of training data input, a sensitivity of model predictions to out-of-distribution (OOD) input data, a posterior distribution of model predictions, prediction confidence scores aggregated across one or more training data sets, a ratio of calculated nearest neighbor distances for interclass and intraclass predictions, one or more model performance metrics, or any combination thereof. In some embodiments, the prediction error estimate is calculated using a loss-based penalty function that is based at least in part on the trust score. In some embodiments, the loss-based penalty function comprises a factor of (2ât), where t is the trust score and has a value of 0â¤tâ¤1. In some embodiments, the prediction error estimate (err) calculation comprises a sum of loss-based penalty function terms each comprising a product of a relative weight for a training data point for which the machine learning model prediction was incorrect and a factor of (2ât). In some embodiments, the prediction error estimate (err) is calculated according to the equation:
e
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r
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r
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i
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1
m
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j
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â
y
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(
2
-
t
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wherein m is a number of labeled training data point pairs in a training data set used to train the machine learning model, D j (i) is a normalized weight for an i th training data point of the j th model, (h(x i )â y i ) is a subset of training data points for which the machine learning model's predicted output value, h(x i ), does not equal a known value, y i , and t is the trust score. In some embodiments, the machine learning model comprises a classifier model. In some embodiments, the classifier model comprises an artificial neural network (ANN), deep learning algorithm (DLA), decision tree algorithm, Naïve Bayes algorithm, support vector machine (SVM), or k-nearest neighbor (KNN) algorithm.
Also disclosed herein are methods for training an ensemble machine learning model comprising: receiving data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; calculating a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; calculating a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and determining an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality.
In some embodiments, the data characterizing a level of trust in each machine learning model of the plurality comprises a trust score for each machine learning model of the plurality. In some embodiments, the trust score is a real number having a value ranging from 0.0 to 1.0. In some embodiments, the trust score for each machine learning model of the plurality is calculated from the received data. In some embodiments, the received data comprises data relating to a sensitivity of model predictions to input data quality, a sensitivity of model predictions to distributional shifts of training data input, a sensitivity of model predictions to out-of-distribution (OOD) input data, a posterior distribution of model predictions, prediction confidence scores aggregated across one or more training data sets, a ratio of calculated nearest neighbor distances for interclass and intraclass predictions, one or more model performance metrics, or any combination thereof. In some embodiments, the prediction error estimate is calculated for each machine learning model of the plurality using a loss-based penalty function for that machine learning model that is based, at least in part, on the trust score for that machine learning model. In some embodiments, the loss-based penalty function for each machine learning model of the plurality comprises a factor of (2ât), where t is the trust score for that machine learning model and has a value of 0â¤tâ¤1. In some embodiments, the prediction error estimate calculation for each machine learning model of the plurality comprises a sum of loss-based penalty function terms each comprising a product of a relative weight for a training data point for which that machine learning model prediction was incorrect and a factor of (2ât), where t is the trust score for that machine learning model. In some embodiments, the prediction error estimate for each machine learning model of the plurality is calculated according to the equation:
e
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r
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r
=
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1
m
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wherein m is a number of labeled training data point pairs in a training data set used to train a given machine learning model of the plurality of machine learning models, D j (i) is a normalized weight for an i th training data point for the j th machine learning model, (h(x i )â y i ) is a subset of training data points for which the given machine learning model's predicted output value, h(x i ), does not equal a known value, y i , and t is the trust score for the given machine learning model. In some embodiments, the output prediction of the ensemble machine learning model is given by the equation:
F
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wherein F(x) is a prediction of the ensemble machine learning model for input data value x, N is a number of machine learning models in the ensemble machine learning model, w i are normalized weights for the plurality of machine learning models that collectively form at least part of the ensemble machine learning model, and f i (x) are predictions of the individual machine learning models in the ensemble for input data value x. In some embodiments, the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, by taking a natural logarithm of a quotient comprising the prediction error estimate for that machine learning model. In some embodiments, the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, according to the equation:
w
i
,
n
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-
normalized
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the priority of U.S. Provisional Application No. 63/228,379, filed Aug. 2, 2021, the entire contents of which are incorporated herein by reference.
FIELD
The present disclosure relates generally to methods for detecting and countering adversarial attacks on machine learning models, and more specifically to methods for incorporating a model trust score when training an ensemble machine learning model.
BACKGROUND
Machine learning (ML) has been adopted across many facets of modern society, with applications ranging from face recognition algorithms used to suggest who to tag in a photo on social media platforms to deep learning algorithms that help with medical diagnoses. While there are a plethora of potential benefits that may be derived from the growing range of ML applications, the increased reliance on ML does not come without risks.
ML algorithms often require vast amounts of data and computational resources to train the machine learning model for a particular application. In order to help alleviate some of the costs associated with data collection and computational resources, publicly available datasets and pre-trained models can be used. While using publicly available datasets and pre-trained models help reduce costs and time, they also come with additional risks. Pre-trained models may be based on data that is not publicly available and/or the source code may not be available to protect intellectual property. This makes it difficult to verify that the model will behave in the expected manner when deployed operationally. If a dataset is large, it can be infeasible to ensure that the dataset is clean and complete. It is known that noisy data, contaminated data, incomplete data, or inherent biases in the data can affect the performance of a machine learning system.
In addition to these non-malicious concerns about machine learning model performance, there are also a growing number of vulnerabilities where an adversary can directly or indirectly attack a ML system such that it affects the system's decision-making outcome. These attacks can be based on the model architecture of the system, the data the system is trained on, or a combination of both. All of these issues lead to concerns about the trustworthiness and accuracy of the machine learning models created.
Ensemble-based machine learning is a common approach that is used to improve accuracy and confidence in ML-based decisions. Ensemble based machine learning is the process of combining multiple models to apply decision-level fusion which can increase the likelihood of making accurate decisions. By using ensemble classifiers, for example, algorithms that are highly accurate but only partially trusted can be incorporated into the ensemble to improve the overall prediction accuracy of the system. Given the primary focus of improved accuracy, little attention has historically been paid to the notion of trust relative to the classifiers incorporated in an ensemble model. Indeed, only a few studies exist that examine the notion of trust for single classifier approaches. Thus, there remains a need to develop methods for incorporating a trust factor in developing and training ensemble machine learning models, and for detecting adversarial attacks that impact the accuracy of the model's predictions.
SUMMARY
Accordingly, disclosed herein are methods for incorporating a trust factor in developing and training ensemble machine learning models, thereby improving the prediction accuracy of the ensemble model, and for detecting adversarial attacks that impact the accuracy of the model's predictions.
Disclosed herein are methods for calculating a prediction error estimate for a machine learning model comprising: receiving data characterizing a level of trust associated with the machine learning model; training the machine learning model on a training data set to determine relative weights for data points in the training data set; and using the data characterizing the level of trust and the relative weights for at least a subset of the data points in the training data set to calculate a prediction error estimate for the machine learning model, wherein the prediction error estimate increases with a decreasing level of trust.
In some embodiments, the data characterizing the level of trust in the machine learning model comprises a trust score. In some embodiments, the trust score is a real number having a value ranging from 0.0 to 1.0. In some embodiments, the trust score is calculated from the received data. In some embodiments, the received data comprises data relating to a sensitivity of model predictions to input data quality, a sensitivity of model predictions to distributional shifts of training data input, a sensitivity of model predictions to out-of-distribution (OOD) input data, a posterior distribution of model predictions, prediction confidence scores aggregated across one or more training data sets, a ratio of calculated nearest neighbor distances for interclass and intraclass predictions, one or more model performance metrics, or any combination thereof. In some embodiments, the prediction error estimate is calculated using a loss-based penalty function that is based at least in part on the trust score. In some embodiments, the loss-based penalty function comprises a factor of (2ât), where t is the trust score and has a value of 0â¤tâ¤1. In some embodiments, the prediction error estimate (err) calculation comprises a sum of loss-based penalty function terms each comprising a product of a relative weight for a training data point for which the machine learning model prediction was incorrect and a factor of (2ât). In some embodiments, the prediction error estimate (err) is calculated according to the equation:
e
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r
=
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i
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wherein m is a number of labeled training data point pairs in a training data set used to train the machine learning model, D j (i) is a normalized weight for an i th training data point of the j th model, (h(x i )â y i ) is a subset of training data points for which the machine learning model's predicted output value, h(x i ), does not equal a known value, y i , and t is the trust score. In some embodiments, the machine learning model comprises a classifier model. In some embodiments, the classifier model comprises an artificial neural network (ANN), deep learning algorithm (DLA), decision tree algorithm, Naïve Bayes algorithm, support vector machine (SVM), or k-nearest neighbor (KNN) algorithm.
Also disclosed herein are methods for training an ensemble machine learning model comprising: receiving data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; calculating a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; calculating a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and determining an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality.
In some embodiments, the data characterizing a level of trust in each machine learning model of the plurality comprises a trust score for each machine learning model of the plurality. In some embodiments, the trust score is a real number having a value ranging from 0.0 to 1.0. In some embodiments, the trust score for each machine learning model of the plurality is calculated from the received data. In some embodiments, the received data comprises data relating to a sensitivity of model predictions to input data quality, a sensitivity of model predictions to distributional shifts of training data input, a sensitivity of model predictions to out-of-distribution (OOD) input data, a posterior distribution of model predictions, prediction confidence scores aggregated across one or more training data sets, a ratio of calculated nearest neighbor distances for interclass and intraclass predictions, one or more model performance metrics, or any combination thereof. In some embodiments, the prediction error estimate is calculated for each machine learning model of the plurality using a loss-based penalty function for that machine learning model that is based, at least in part, on the trust score for that machine learning model. In some embodiments, the loss-based penalty function for each machine learning model of the plurality comprises a factor of (2ât), where t is the trust score for that machine learning model and has a value of 0â¤tâ¤1. In some embodiments, the prediction error estimate calculation for each machine learning model of the plurality comprises a sum of loss-based penalty function terms each comprising a product of a relative weight for a training data point for which that machine learning model prediction was incorrect and a factor of (2ât), where t is the trust score for that machine learning model. In some embodiments, the prediction error estimate for each machine learning model of the plurality is calculated according to the equation:
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wherein m is a number of labeled training data point pairs in a training data set used to train a given machine learning model of the plurality of machine learning models, D j (i) is a normalized weight for an i th training data point for the j th machine learning model, (h(x i )â y i ) is a subset of training data points for which the given machine learning model's predicted output value, h(x i ), does not equal a known value, y i , and t is the trust score for the given machine learning model. In some embodiments, the output prediction of the ensemble machine learning model is given by the equation:
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wherein F(x) is a prediction of the ensemble machine learning model for input data value x, N is a number of machine learning models in the ensemble machine learning model, w i are normalized weights for the plurality of machine learning models that collectively form at least part of the ensemble machine learning model, and f i (x) are predictions of the individual machine learning models in the ensemble for input data value x. In some embodiments, the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, by taking a natural logarithm of a quotient comprising the prediction error estimate for that machine learning model. In some embodiments, the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, according to the equation:
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wherein err i is the prediction error estimate calculated for the i th machine learning model of the plurality, wherein
w i =w i,non-normalized /Σ i=1 N w i,non-normalized
and wherein N is a number of individual machine learning models in the ensemble machine learning model. In some embodiments, the normalized weights for the individual machine learning models of the ensemble machine learning model are calculated by: reformulating the output prediction equation in the form of a quadratic unconstrained binary optimization (QUBO) problem; and using a quantum computing method to solve the QUBO problem for the normalized weights, w i , for the one or more machine learning models. In some embodiments, the method further comprises receiving additional data characterizing levels of trust in one or more machine learning models of the plurality and re-adjusting the output prediction equation for the ensemble if a change in a level of trust is detected for one or more machine learning models of the plurality. In some embodiments, one or more of the machine learning models of the plurality of machine learning models comprises a classifier model. In some embodiments, the classifier model comprises an artificial neural network (ANN), deep learning algorithm (DLA), decision tree algorithm, Naïve Bayes algorithm, support vector machine (SVM), or k-nearest neighbor (KNN) algorithm. In some embodiments, the ensemble machine learning model is trained using an AdaBoost method.
Disclosed herein are methods for training an ensemble machine learning model comprising: receiving data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; training individual machine learning models of the ensemble machine learning model using an AdaBoost method, wherein the training comprises the use of a loss-based penalty function for each machine learning model of the plurality to calculate a prediction error estimate for that machine learning model, and wherein the prediction error estimate is based on a trust score for that machine learning model and relative weights calculated for at least a subset of data points in a training data set used to train that machine learning model; calculating a normalized weight for each individual machine learning model of the ensemble; and determining an output prediction equation for the ensemble machine learning model, wherein the normalized weights calculated for each individual machine learning model are used to formulate the output prediction equation for the ensemble machine learning model.
In some embodiments, the method further comprises formulating the output prediction equation for the ensemble machine learning model as a sum of two terms: an exponential loss function term that provides a measure of a total number of errors made by the ensemble machine learning model as a function of the normalized weights, w i , for the individual machine learning models of the ensemble in predicting a result, yâ² s , for a given input value, x s , when processing a training data set comprising labeled training data points, (x s , y s ); and a regularization term that comprises a product of (i) a sum of non-zero normalized weights, w i 0 , for the individual of machine learning models of the ensemble and (ii) a control variable, λ; and minimizing the two terms of the output prediction equation to determine the normalized weights, w i , for the plurality of machine learning models. In some embodiments, the minimizing is performed by converting the normalized weights, w i , for the plurality of machine learning models to binary values using a binary expansion; rewriting the exponential loss function as a quadratic loss function; expanding and combining the quadratic loss function term, the binary values of the normalized weights, w i , and the regularization term to formulate a quadratic unconstrained binary optimization (QUBO) problem; and solving the QUBO problem using a quantum computing platform. In some embodiments, the ensemble machine learning model is a binary classifier. In some embodiments, the binary values derived from binary expansion of the normalized weights, w i , for the plurality of machine learning models comprise qubits. In some embodiments, the minimum number of qubits, b, required for the binary expansion is given by bâ¤log 2 (f)+log 2 (e)â1, where e is Euler's number, f=S/N, S is the number of training data point pairs, and N is the number of individual machine learning models in the ensemble machine learning model. In some embodiments, b<32. In some embodiments, b=1. In some embodiments, the quadratic unconstrained binary optimization (QUBO) is expressed as:
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wherein w opt is a set of optimized weights for a binary classifier which is used to weight predictions of the individual machine learning models. In some embodiments, the method further comprises receiving additional data characterizing levels of trust in one or more machine learning models of the plurality and re-calculating the normalized weight for each individual machine learning model of the ensemble if a change in a level of trust is detected for one or more machine learning models of the plurality. In some embodiments, the quantum computing platform comprises an Amazon Bracket, Azure Quantum, D-Wave, or TensorFlow Quantum computing platform.
Disclosed herein are systems comprising: one or more processors; memory; and one or more programs stored in the memory and comprising instructions that, when executed by the one or more processors, cause the one or more processors to: a) receive data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; b) calculate a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; c) calculate a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and d) determine an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality. In some embodiments, the one or more programs further comprise instructions that, when executed by the one or more processors, cause the one or more processors to perform any of the methods disclosed herein.
Also disclosed are non-transitory, computer-readable media storing one or more programs, the one or more programs comprising instructions which, when executed by one or more processors of an electronic device or system, cause the electronic device or system to: a) receive data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; b) calculate a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; c) calculate a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and d) determine an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality. In some embodiments, the one or more programs further comprise instructions that, when executed by the one or more processors, cause the electronic device or system to perform any of the methods disclosed herein.
INCORPORATION BY REFERENCE
All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference in their entirety to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference in its entirety. In the event of a conflict between a term herein and a term in an incorporated reference, the term herein controls.
BRIEF DESCRIPTION OF THE FIGURES
Various aspects of the disclosed methods, devices, and systems are set forth with particularity in the appended claims. A better understanding of the features and advantages of the disclosed methods, devices, and systems will be obtained by reference to the following detailed description of illustrative embodiments and the accompanying drawings, of which:
FIG. 1 A provides a schematic illustration of where an ensemble-based machine learning model comprising a trust score fits in the adversarial attack landscape.
FIG. 1 B provides a schematic illustration of an ensemble-based machine learning model comprising a trust score.
FIG. 2 provides a schematic illustration of using, e.g., the accuracies and trust scores of the individual models that form an ensemble-based machine learning model (1) to adjust model prediction accuracy (2), where a quantum computing approach (3) is used to train the ensemble model.
FIG. 3 provides a schematic illustration of the use of both trusted (C1-C3 and C7-C8) and untrusted (C4-C6) machine learning models can be used to create an ensemble machine learning model where the trust scores for the individual models are used to improve the accuracy of the final prediction.
FIG. 4 A provides a schematic illustration of the concepts of accuracy and trustworthiness for machine learning model predictions.
FIG. 4 B provides a schematic illustration of an approach for determining a trust score for a classifier based on a nearest neighbor distance calculation for interclass and intraclass predictions for a training data set.
FIG. 5 provides a schematic illustration of a machine learning architecture comprising an artificial neural network with one hidden layer.
FIG. 6 provides a schematic illustration of a node within a layer of an artificial neural network or deep learning algorithm architecture.
FIG. 7 provides a non-limiting example of a workflow for detecting adversarial attacks on an ensemble machine learning model using trust scores, and mitigating the effects of the attack by rapidly updating the output prediction equation for the ensemble model.
FIG. 8 provides a non-limiting example of a computing device in accordance with one or more examples of the disclosure.
FIG. 9 provides a schematic illustration of a quantum computing platform (adapted from Gill, et al. (2020), âQuantum computing: a taxonomy, systematic review and future directionsâ, arXiv:2010.15559).
DETAILED DESCRIPTION
The disclosed methods provide a novel approach to securely integrating untrusted machine learning models, e.g., classifiers, in ensemble-based machine learning models to improve the prediction accuracy of the ensemble model and estimate prediction error. By applying a penalty function based on individual classifier trust levels, one is able to incorporate classifiers into an ensemble that individually may often be accurate but may sometimes be untrustworthy. One can then map the process of computing a conditioned weight for the individual machine learning models that factors in the trust component to a problem that can be solved on the hardware of a quantum computer. These conditioned weights from all models in the ensemble can then be fused using a variety of approaches to improve the accuracy and trustworthiness of the ensemble model prediction.
The primary objectives in developing the disclosed methods were to (i) improve the prediction accuracy of ensemble machine learning models that include partially trustworthy models, (ii) increase the reliability and speed with which the conditioning process for adjusting the relative weights for models in the ensemble can be completed by execution on a quantum computing platform, and (iii) develop a means for efficient detection of adversarial activity in ensemble-based artificial intelligence (AI)/machine learning (ML) models that condition the predictions from individual models using a trust score.
FIG. 1 B provides a schematic illustration of an ensemble-based machine learning model comprising a trust score to adjust the relative weight of the individual models in influencing the output prediction of the ensemble model. FIG. 1 A illustrates where such ensemble models fit in the adversarial attack landscape. Adversarial attacks may comprise targeted attacks (in which the attack redirects the model prediction to a specific class) or non-targeted attacks (in which the attack does not redirect the model prediction to a specific class) on the model architecture and/or on the model data. âBlack boxâ attacks are attacks in which an adversary does not have access to the trained model. FIG. 1 A provides non-limiting examples of attack types that target AI/ML model architecture and those that target the trained model or exemplar data.
FIG. 2 provides a schematic illustration of using, e.g., the accuracies and trust scores of the individual models that form an ensemble-based machine learning model (1) to adjust model prediction accuracy (2), where a quantum computing approach (3) is used to train the ensemble model. In some instances, the disclosed methods for incorporating a trust score into the training and/or execution of an ensemble machine learning model may enable detection of adversarial attacks.
FIG. 3 provides a schematic illustration of the use of both trusted (C1-C3 and C7-C8) and untrusted (C4-C6) machine learning models can be used to create an ensemble machine learning model where the trust scores for the individual models are used to improve the accuracy of the final prediction. In the context of machine learning, the concept of âtrustâ may be thought of as a characterization of how reliably/consistently a model performs. A trust score can include a measure of the consistency and/or reliability of model predictions. As illustrated in FIG. 4 A , âaccuracyâ (e.g., the circles in FIG. 4 A ) may be thought of as a measure of the correctness of a model's predictions, while âtrustworthinessâ (e.g., the points in FIG. 4 A ) may be thought of as a measure of the precision (or standard deviation) of a model's predictions. As will be discussed in more detail below, the implementation of a new loss function comprising a factor of (2ât), where t is the trust score for an individual model, may be used to calculate the training error exhibited by a given model which in turn may be used to adjust the relative weight of the individual models in influencing the output prediction of the ensemble model.
Ensemble-based machine learning approaches are becoming increasingly popular in the world of machine learning and artificial intelligence applications, and there is a need to know whether or not decisions made by ensemble-based models are trustworthy. Specifically, when constructing an ensemble model one may wish to include, e.g., classifiers that are only moderately accurate but extremely trustworthy, and also classifiers that are usually highly accurate but occasionally untrustworthy. The disclosed methods allow one to integrate these untrustworthy classifiers, and leverage their accuracy when acting in a trustworthy fashion, but discount their predictions when they appear not to be acting trustworthy.
In a first aspect of the present disclosure, a new loss-based penalty function based on a trust score for a given machine learning model is provided for use in evaluating a normalized weight (or weighting factor) for the model when incorporating the model into an ensemble machine learning approach. As noted above, the new loss-based penalty function comprises a factor of (2ât), where t is the trust score for the given model. In some instances, the trust score may be an empirically-derived quantity having, e.g., a real value ranging from 0.0 (untrustworthy) to 1.0 (trusted). In some instances, a trust score may reflect the source and pedigree of a machine learning model rather than its accuracy metrics and may include, for example, verification of the source code for a given model, etc. In some instances, a trust score may be calculated from data received for a given model based on model-dependent and data-dependent factors such as the quality of the data (e.g., the amount of noise in the data, contamination of the data, the completeness of the data, etc.), the sensitivity of the given model architecture to the quality of the data, the frequency of prediction mistakes made by the given model when processing a defined test dataset, etc., or any combination thereof.
Non-limiting examples of approaches that may be used in determining a trust score for a machine learning model have been described in the literature, see for example, Jiang, et al. (2018), âTo Trust Or Not To Trust A Classifierâ, 32 nd Conference on Neural Information Processing Systems (NIPS 2018), Montreal, Canada; and Ovadia, et al. (2019), âCan You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftâ, 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada. Some approaches may include, for example, modeling the posterior probability distributions of classifier predictions and looking at the uncertainty in model predictions to determine a trust score. Other approaches may include, for example, examining prediction confidence scores derived from the model itself, and aggregating confidence scores across a plurality of training data sets to determine a trust score. Yet other approaches may evaluate the robustness of model predictions to distributional shifts of the input data and out-of-distribution (OOD) inputs. In some instances, a trust score may be derived on the basis of one or more model performance metrics, including metrics that do not depend on predictive uncertainty (e.g., classification accuracy), and metrics that do depend on predictive uncertainty (e.g., negative log-likelihood (NLL) and Brier Score (Ovadia, et al. (2019), ibid.).
Another non-limiting example of an approach for determining a trust score (see, e.g., Jiang, et al. (2018), ibid.) involves looking at class boundaries (or decision boundaries) in the training data. As illustrated in FIG. 4 B for a multiclass image classifier trained to classify images of dogs, cats, and horses, one may calculate a distance, M 1 , between a sample prediction and the closest interclass prediction (i.e., a prediction for a different input sample). One may also calculate a distance, M 2 , between the sample prediction and the next closest intraclass prediction (i.e., a prediction for the same class). A trust score for the prediction can then be determined based on the ratio M 1 /M 2 . Aggregating the trust scores for individual predictions across all input samples may then be used to determine a trust score for the model. In some instances, one may draw on similarities between this approach and applications in Explainable AI, e.g., methods involving heat maps that, if fused with this approach, may lead to a more model-agnostic solution.
In some instances, the trust score may be recalculated for a given machine learning model, e.g., at periodic or random time intervals (or continuously), or based on other triggers, to detect changes in the trust score. In some instances, the detection of a change in the trust score for the given machine learning model may be indicative of an adversarial attack on the machine learning model. Examples of conditions that might trigger a recalculation of trust score include, but are not limited to, a detection of data drift (e.g., if a model's predictions have deviated from the expected results for a submitted set of test data, or if the predictions of an ensemble model no longer reflect the expected output for the training data).
As noted above, the disclosed methods provide for improved accuracy of prediction by ensemble machine learning models that may include partially trustworthy individual models. In some instances, the disclosed methods may comprise adjusting (e.g., automatically adjusting) the relative weights for one or more individual models in an ensemble, e.g., upon detection of a change in one or more of their respective trust scores. In some instances, the disclosed methods may comprise including or excluding (e.g., automatically including or excluding) individual models from the ensemble based on their respective trustworthiness, e.g., based on their respective trust scores or upon detection of a change in their respective trust scores. In some instances, detection of a change in trust score may trigger investigation of a potential adversarial attack. In some instances, detection of a change in trust score may constitute detection of an adversarial attack.
In a second aspect of the present disclosure, a method for incorporating individual model trust scores into an ensemble-based machine learning system to weight their relative contributions and improve the ensemble model's prediction accuracy is disclosed. As will be discussed in more detail below, the trust scores for one or more machine learning models of a plurality of models that collectively constitute an ensemble-based machine learning model may be used to define loss-based penalty functions for each individual model, which in turn may be used to determine normalized weights for the one or more machine learning models of the plurality. The normalized weights may then be used to weight the relative contributions of the individual models to the ensemble model's output prediction. In some instances, the trust score may be recalculated for one or more machine learning models in an ensemble model, e.g., at random or periodic intervals (or continuously), to detect changes in the trust score for the one or more machine learning models. In some instances, the detection of a change in the trust score for one or more machine learning models in an ensemble model may be indicative of an adversarial attack on the one or more machine learning models or on the ensemble model. In some instances, the detection of a change in the trust score for one or more machine learning models in an ensemble model may be used to update the relative weight(s) of the one or more machine learning models and adjust its contribution to the output prediction of the ensemble model.
In a third aspect of the present disclosure, a method for reformulating the trust score-weighted final output prediction equation for an ensemble-based machine learning model as a quadratic unconstrained binary optimization (QUBO) problem that may be solved for the relative weights of the individual models on a quantum computing platform is provided. In some instances, the ability to formulate the trust score-based conditioning of the ensemble model as a QUBO problem suitable for solving with, e.g., Qboost (large scale classifier training with adiabatic quantum optimization) on a quantum computing platform may greatly increase the speed with which the model training converges to a solution. To date, other approaches to factoring in a trust-score in ensemble machine learning have taken other approaches, e.g., application of various neural networks and support vector machines. In some instances, the disclosed methods for formulating the trust score-based conditioning of the ensemble model as a QUBO problem to be solved on a quantum computing platform may allow not only real-time (or near real-time) detection of adversarial attacks on the ensemble model (based on detected changes in trust scores), but also recalculation of the relative weights for the individual models and adjustment of their contributions to the output prediction of the ensemble model in real-time (or near real-time). The disclosed methods and systems thus may provide significant advantages over current methods for detection and mitigation of adversarial attacks on ensemble machine learning models.
Definitions: Unless otherwise defined, all of the technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art in the field to which this disclosure belongs.
As used in this specification and the appended claims, the singular forms âaâ, âanâ, and âtheâ include plural references unless the context clearly dictates otherwise. Any reference to âorâ herein is intended to encompass âand/orâ unless otherwise stated.
As used herein, the terms âcomprisingâ (and any form or variant of comprising, such as âcompriseâ and âcomprisesâ), âhavingâ (and any form or variant of having, such as âhaveâ and âhasâ), âincludingâ (and any form or variant of including, such as âincludesâ and âincludeâ), or âcontainingâ (and any form or variant of containing, such as âcontainsâ and âcontainâ), are inclusive or open-ended and do not exclude additional, un-recited additives, components, integers, elements or method steps.
As used herein, the term âaboutâ a number refers to that number plus or minus 10% of that number. The term âaboutâ when used in the context of a range refers to that range minus 10% of its lowest value and plus 10% of its greatest value.
As used herein, the term âaccuracyâ may refer to a statistical measure of how well a trained binary classification model correctly classifies an input data set into the defined output classes.
As used herein, the term âreal-timeâ may refer to the rate at which data is acquired, input to, and/or processed by a machine learning or artificial intelligence to update, e.g., a prediction, a decision, a control signal, a set of instructions, or other form of output, in response to a change in one or more input data streams such that there is no delay or a minimal delay between a change in one or more input data streams and the update of the prediction, decision, control signal, set of instructions, or other form of output.
As used herein, the term âmachine learningâ may refer to the use of any of a variety of algorithms known to those of skill in the art that may be trained to process input data and map it to a learned output, e.g., a prediction, decision, control signal, or set of instructions. In some instances, the term âartificial intelligenceâ may be used interchangeably with the term âmachine learningâ.
As used herein, the term âneural networkâ may refer either to a specific machine learning algorithm, e.g., an artificial neural network (ANN) or deep learning algorithm, or more generally to a system, e.g., a cloud-based system, designed to implement any of the machine learning-based methods disclosed herein.
The section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.
Machine learning algorithms: Any of a variety of machine learning algorithms may be used in implementing the disclosed methods and systems, either as stand-alone machine learning models or as components of an ensemble machine learning model. For example, the machine learning algorithm(s) employed may comprise supervised learning algorithms, unsupervised learning algorithms, semi-supervised learning algorithms, deep learning algorithms, or any combination thereof. In some instances, the machine learning algorithm(s) employed may comprise, e.g., an artificial neural network algorithm, a Gaussian process regression algorithm, a logistical model tree algorithm, a random forest algorithm, a fuzzy classifier algorithm, a decision tree algorithm, a hierarchical clustering algorithm, a Naïve Bayes algorithm, a k-nearest neighbor (KNN) algorithm, a k-means algorithm, a fuzzy clustering algorithm, a deep Boltzmann machine learning algorithm, a deep convolutional neural network algorithm, a deep recurrent neural network, or any combination thereof, several of which will be described in more detail below.
Supervised learning algorithms: Supervised learning algorithm
CLAIMS
Claims ( 30 )
What is claimed is:
1 . A method for training an ensemble machine learning model comprising:
a) receiving data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; b) calculating a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; c) calculating a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and d) determining an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality.
2 . The method of claim 1 , wherein the data characterizing a level of trust in each machine learning model of the plurality comprises a trust score for each machine learning model of the plurality.
3 . The method of claim 2 , wherein the trust score is a real number having a value ranging from 0.0 to 1.0.
4 . The method of claim 2 , wherein the trust score for each machine learning model of the plurality is calculated from the received data.
5 . The method of claim 4 , wherein the received data comprises data relating to a sensitivity of model predictions to input data quality, a sensitivity of model predictions to distributional shifts of training data input, a sensitivity of model predictions to out-of-distribution (OOD) input data, a posterior distribution of model predictions, prediction confidence scores aggregated across one or more training data sets, a ratio of calculated nearest neighbor distances for interclass and intraclass predictions, one or more model performance metrics, or any combination thereof.
6 . The method of claim 1 , wherein the prediction error estimate is calculated for each machine learning model of the plurality using a loss-based penalty function for that machine learning model that is based, at least in part, on the trust score for that machine learning model.
7 . The method of claim 6 , wherein the loss-based penalty function for each machine learning model of the plurality comprises a factor of (2ât), where t is the trust score for that machine learning model and has a value of 0â¤tâ¤1.
8 . The method of claim 7 , wherein the prediction error estimate calculation for each machine learning model of the plurality comprises a sum of loss-based penalty function terms each comprising a product of a relative weight for a training data point for which that machine learning model prediction was incorrect and a factor of (2ât), where t is the trust score for that machine learning model.
9 . The method of claim 8 , wherein the prediction error estimate for each machine learning model of the plurality is calculated according to the equation:
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wherein m is a number of labeled training data point pairs in a training data set used to train a given machine learning model of the plurality of machine learning models, D j (i) is a normalized weight for an i th training data point for the j th machine learning model, (h(x i )â y i ) is a subset of training data points for which the given machine learning model's predicted output value, h(x i ), does not equal a known value, y i , and t is the trust score for the given machine learning model.
10 . The method of claim 1 , wherein the output prediction of the ensemble machine learning model is given by the equation:
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wherein F(x) is a prediction of the ensemble machine learning model for input data value x, N is a number of machine learning models in the ensemble machine learning model, w i are normalized weights for the plurality of machine learning models that collectively form at least part of the ensemble machine learning model, and f i (x) are predictions of the individual machine learning models in the ensemble for input data value x.
11 . The method of claim 10 , wherein the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, by taking a natural logarithm of a quotient comprising the prediction error estimate for that machine learning model.
12 . The method of claim 11 , wherein the normalized weight, w i , for each machine learning model of the plurality is calculated, at least in part, according to the equation:
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wherein err i is the prediction error estimate calculated for the i th machine learning model of the plurality, wherein
w i =w i,non-normalized /Σ i=1 N w i,non-normalized
and wherein N is a number of individual machine learning models in the ensemble machine learning model.
13 . The method of claim 10 , wherein the normalized weights for the individual machine learning models of the ensemble machine learning model are calculated by:
a) reformulating the output prediction equation in the form of a quadratic unconstrained binary optimization (QUBO) problem; and b) using a quantum computing method to solve the QUBO problem for the normalized weights, w i , for the one or more machine learning models.
14 . The method of claim 1 , further comprising receiving additional data characterizing levels of trust in one or more machine learning models of the plurality and re-adjusting the output prediction equation for the ensemble if a change in a level of trust is detected for one or more machine learning models of the plurality.
15 . The method of claim 1 , wherein one or more of the machine learning models of the plurality of machine learning models comprises a classifier model.
16 . The method of claim 15 , wherein the classifier model comprises an artificial neural network (ANN), deep learning algorithm (DLA), decision tree algorithm, Naïve Bayes algorithm, support vector machine (SVM), or k-nearest neighbor (KNN) algorithm.
17 . The method of claim 1 , wherein the ensemble machine learning model is trained using an AdaBoost method.
18 . A method for training an ensemble machine learning model comprising:
a) receiving data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; b) training individual machine learning models of the ensemble machine learning model using an AdaBoost method, wherein the training comprises the use of a loss-based penalty function for each machine learning model of the plurality to calculate a prediction error estimate for that machine learning model, and wherein the prediction error estimate is based on a trust score for that machine learning model and relative weights calculated for at least a subset of data points in a training data set used to train that machine learning model; and c) calculating a normalized weight for each individual machine learning model of the ensemble; and d) determining an output prediction equation for the ensemble machine learning model, wherein the normalized weights calculated in (c) are used to formulate the output prediction equation for the ensemble machine learning model.
19 . The method of claim 18 , further comprising formulating the output prediction equation for the ensemble machine learning model as a sum of two terms:
a) an exponential loss function term that provides a measure of a total number of errors made by the ensemble machine learning model as a function of the normalized weights, w i , for the individual machine learning models of the ensemble in predicting a result, yⲠs , for a given input value, x s , when processing a training data set comprising labeled training data points, (x s , y s ); and b) a regularization term that comprises a product of (i) a sum of non-zero normalized weights, w i 0 , for the individual of machine learning models of the ensemble and (ii) a control variable, λ; and
minimizing the two terms of the output prediction equation to determine the normalized weights, w i , for the plurality of machine learning models.
20 . The method of claim 19 , wherein the minimizing is performed by
a) converting the normalized weights, w i , for the plurality of machine learning models to binary values using a binary expansion; b) rewriting the exponential loss function as a quadratic loss function; c) expanding and combining the quadratic loss function term, the binary values of the normalized weights, w i , and the regularization term to formulate a quadratic unconstrained binary optimization (QUBO) problem; and d) solving the QUBO problem using a quantum computing platform.
21 . The method of claim 18 , wherein the ensemble machine learning model is a binary classifier.
22 . The method of claim 20 , wherein the binary values derived from binary expansion of the normalized weights, w i , for the plurality of machine learning models comprise qubits.
23 . The method of claim 22 , wherein the minimum number of qubits, b, required for the binary expansion is given by bâ¥log 2 (f)+log2(e)â1, where e is Euler's number, f=S/N, S is the number of training data point pairs, and N is the number of individual machine learning models in the ensemble machine learning model.
24 . The method of claim 23 , wherein b<32.
25 . The method of claim 23 , wherein b=1.
26 . The method of claim 25 , wherein the quadratic unconstrained binary optimization (QUBO) is expressed as:
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wherein w opt is a set of optimized weights for a binary classifier which is used to weight predictions of the individual machine learning models.
27 . The method of claim 18 , further comprising receiving additional data characterizing levels of trust in one or more machine learning models of the plurality and re-calculating the normalized weight for each individual machine learning model of the ensemble if a change in a level of trust is detected for one or more machine learning models of the plurality.
28 . The method of claim 20 , wherein the quantum computing platform comprises an Amazon Bracket, Azure Quantum, D-Wave, or TensorFlow Quantum quantum computing platform.
29 . A system comprising:
one or more processors; memory; and one or more programs stored in the memory and comprising instructions that, when executed by the one or more processors, cause the one or more processors to:
a) receive data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model;
b) calculate a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model;
c) calculate a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and
d) determine an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality.
30 . A non-transitory, computer-readable medium storing one or more programs, the one or more programs comprising instructions which, when executed by one or more processors of an electronic device or system, cause the electronic device or system to:
a) receive data characterizing levels of trust in a plurality of machine learning models, wherein the plurality of machine learning models collectively form at least part of the ensemble machine learning model; b) calculate a prediction error estimate for each machine learning model of the plurality, wherein the prediction error estimate for each machine learning model is based on a trust score for that machine learning model and relative weights calculated for at least a subset of the data points in a training data set used to train that machine learning model; c) calculate a normalized weight for each machine learning model of the plurality using the prediction error estimate calculated in (b) for each machine learning model of the plurality; and d) determine an output prediction equation for the ensemble machine learning model, wherein the determination is based, at least in part, on the normalized weights calculated in (c) for each machine learning model of the plurality.
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