Algorithms such as Differentially Private SGD enable training machine learning models with formal privacy guarantees. However, there is a discrepancy between the protection that such algorithms guarantee in theory and the protection they afford in practice. An emerging strand of work empirically estimates the protection afforded by differentially private training as a confidence interval for the privacy budget $\varepsilon$ spent on training a model. Existing approaches derive confidence intervals for $\varepsilon$ from confidence intervals for the false positive and false negative rates of membership inference attacks. Unfortunately, obtaining narrow high-confidence intervals for $\epsilon$ using this method requires an impractically large sample size and training as many models as samples. We propose a novel Bayesian method that greatly reduces sample size, and adapt and validate a heuristic to draw more than one sample per trained model. Our Bayesian method exploits the hypothesis testing interpretation of differential privacy to obtain a posterior for $\varepsilon$ (not just a confidence interval) from the joint posterior of the false positive and false negative rates of membership inference attacks. For the same sample size and confidence, we derive confidence intervals for $\varepsilon$ around 40% narrower than prior work. The heuristic, which we adapt from label-only DP, can be used to further reduce the number of trained models needed to get enough samples by up to 2 orders of magnitude.
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In this paper, we show that the process of continually learning new tasks and memorizing previous tasks introduces unknown privacy risks and challenges to bound the privacy loss. Based upon this, we introduce a formal definition of Lifelong DP, in which the participation of any data tuples in the training set of any tasks is protected, under a consistently bounded DP protection, given a growing stream of tasks. A consistently bounded DP means having only one fixed value of the DP privacy budget, regardless of the number of tasks. To preserve Lifelong DP, we propose a scalable and heterogeneous algorithm, called L2DP-ML with a streaming batch training, to efficiently train and continue releasing new versions of an L2M model, given the heterogeneity in terms of data sizes and the training order of tasks, without affecting DP protection of the private training set. An end-to-end theoretical analysis and thorough evaluations show that our mechanism is significantly better than baseline approaches in preserving Lifelong DP. The implementation of L2DP-ML is available at: //github.com/haiphanNJIT/PrivateDeepLearning.
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional settings. This paper shows that standard notions of statistical depth, i.e., halfspace depth and regression depth, are particularly advantageous in this regard, both in the sense that the maximum influence of a single observation is easy to analyze and that this value is typically low. This is used to motivate new approximate DP location and regression estimators using the maximizers of these two notions of statistical depth. A more computationally efficient variant of the approximate DP regression estimator is also provided. Also, to avoid requiring that users specify a priori bounds on the estimates and/or the observations, variants of these DP mechanisms are described that satisfy random differential privacy (RDP), which is a relaxation of differential privacy provided by Hall, Wasserman, and Rinaldo (2013). We also provide simulations of the two DP regression methods proposed here. The proposed estimators appear to perform favorably relative to the existing DP regression methods we consider in these simulations when either the sample size is at least 100-200 or the privacy-loss budget is sufficiently high.
Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.
Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is tackling their ill-posed nature. Bayesian inference provides a principled approach for overcoming this by formulating the inverse problem into a statistical framework. However, it is challenging to apply when inferring fields that have discrete representations of large dimensions (the so-called "curse of dimensionality") and/or when prior information is available only in the form of previously acquired solutions. In this work, we present a novel method for efficient and accurate Bayesian inversion using deep generative models. Specifically, we demonstrate how using the approximate distribution learned by a Generative Adversarial Network (GAN) as a prior in a Bayesian update and reformulating the resulting inference problem in the low-dimensional latent space of the GAN, enables the efficient solution of large-scale Bayesian inverse problems. Our statistical framework preserves the underlying physics and is demonstrated to yield accurate results with reliable uncertainty estimates, even in the absence of information about underlying noise model, which is a significant challenge with many existing methods. We demonstrate the effectiveness of proposed method on a variety of inverse problems which include both synthetic as well as experimentally observed data.
Context: Differential testing is a useful approach that uses different implementations of the same algorithms and compares the results for software testing. In recent years, this approach was successfully used for test campaigns of deep learning frameworks. Objective: There is little knowledge on the application of differential testing beyond deep learning. Within this article, we want to close this gap for classification algorithms. Method: We conduct a case study using Scikit-learn, Weka, Spark MLlib, and Caret in which we identify the potential of differential testing by considering which algorithms are available in multiple frameworks, the feasibility by identifying pairs of algorithms that should exhibit the same behavior, and the effectiveness by executing tests for the identified pairs and analyzing the deviations. Results: While we found a large potential for popular algorithms, the feasibility seems limited because often it is not possible to determine configurations that are the same in other frameworks. The execution of the feasible tests revealed that there is a large amount of deviations for the scores and classes. Only a lenient approach based on statistical significance of classes does not lead to a huge amount of test failures. Conclusions: The potential of differential testing beyond deep learning seems limited for research into the quality of machine learning libraries. Practitioners may still use the approach if they have deep knowledge about implementations, especially if a coarse oracle that only considers significant differences of classes is sufficient.
The majority of recent state-of-the-art speaker verification architectures adopt multi-scale processing and frequency-channel attention mechanisms. Convolutional layers of these models typically have a fixed kernel size, e.g., 3 or 5. In this study, we further contribute to this line of research utilising a selective kernel attention (SKA) mechanism. The SKA mechanism allows each convolutional layer to adaptively select the kernel size in a data-driven fashion. It is based on an attention mechanism which exploits both frequency and channel domain. We first apply existing SKA module to our baseline. Then we propose two SKA variants where the first variant is applied in front of the ECAPA-TDNN model and the other is combined with the Res2net backbone block. Through extensive experiments, we demonstrate that our two proposed SKA variants consistently improves the performance and are complementary when tested on three different evaluation protocols.
Given a partial differential equation (PDE), goal-oriented error estimation allows us to understand how errors in a diagnostic quantity of interest (QoI), or goal, occur and accumulate in a numerical approximation, for example using the finite element method. By decomposing the error estimates into contributions from individual elements, it is possible to formulate adaptation methods, which modify the mesh with the objective of minimising the resulting QoI error. However, the standard error estimate formulation involves the true adjoint solution, which is unknown in practice. As such, it is common practice to approximate it with an 'enriched' approximation (e.g. in a higher order space or on a refined mesh). Doing so generally results in a significant increase in computational cost, which can be a bottleneck compromising the competitiveness of (goal-oriented) adaptive simulations. The central idea of this paper is to develop a "data-driven" goal-oriented mesh adaptation approach through the selective replacement of the expensive error estimation step with an appropriately configured and trained neural network. In doing so, the error estimator may be obtained without even constructing the enriched spaces. An element-by-element construction is employed here, whereby local values of various parameters related to the mesh geometry and underlying problem physics are taken as inputs, and the corresponding contribution to the error estimator is taken as output. We demonstrate that this approach is able to obtain the same accuracy with a reduced computational cost, for adaptive mesh test cases related to flow around tidal turbines, which interact via their downstream wakes, and where the overall power output of the farm is taken as the QoI. Moreover, we demonstrate that the element-by-element approach implies reasonably low training costs.
Deep learning plays a more and more important role in our daily life due to its competitive performance in multiple industrial application domains. As the core of DL-enabled systems, deep neural networks automatically learn knowledge from carefully collected and organized training data to gain the ability to predict the label of unseen data. Similar to the traditional software systems that need to be comprehensively tested, DNNs also need to be carefully evaluated to make sure the quality of the trained model meets the demand. In practice, the de facto standard to assess the quality of DNNs in industry is to check their performance (accuracy) on a collected set of labeled test data. However, preparing such labeled data is often not easy partly because of the huge labeling effort, i.e., data labeling is labor-intensive, especially with the massive new incoming unlabeled data every day. Recent studies show that test selection for DNN is a promising direction that tackles this issue by selecting minimal representative data to label and using these data to assess the model. However, it still requires human effort and cannot be automatic. In this paper, we propose a novel technique, named Aries, that can estimate the performance of DNNs on new unlabeled data using only the information obtained from the original test data. The key insight behind our technique is that the model should have similar prediction accuracy on the data which have similar distances to the decision boundary. We performed a large-scale evaluation of our technique on 13 types of data transformation methods. The results demonstrate the usefulness of our technique that the estimated accuracy by Aries is only 0.03% -- 2.60% (on average 0.61%) off the true accuracy. Besides, Aries also outperforms the state-of-the-art selection-labeling-based methods in most (96 out of 128) cases.
The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.
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