Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen widespread use in machine learning. In this work, we aim to bridge this gap by exploring the use of tilting in risk minimization. We study a simple extension to ERM -- tilted empirical risk minimization (TERM) -- which uses exponential tilting to flexibly tune the impact of individual losses. The resulting framework has several useful properties: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to the tail probability of losses. Our work makes rigorous connections between TERM and related objectives, such as Value-at-Risk, Conditional Value-at-Risk, and distributionally robust optimization (DRO). We develop batch and stochastic first-order optimization methods for solving TERM, provide convergence guarantees for the solvers, and show that the framework can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications in machine learning, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. Despite the straightforward modification TERM makes to traditional ERM objectives, we find that the framework can consistently outperform ERM and deliver competitive performance with state-of-the-art, problem-specific approaches.
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Neglected tropical diseases (NTDs) continue to affect the livelihood of individuals in countries in the Southeast Asia and Western Pacific region. These diseases have been long existing and have caused devastating health problems and economic decline to people in low- and middle-income (developing) countries. An estimated 1.7 billion of the world's population suffer one or more NTDs annually, this puts approximately one in five individuals at risk for NTDs. In addition to health and social impact, NTDs inflict significant financial burden to patients, close relatives, and are responsible for billions of dollars lost in revenue from reduced labor productivity in developing countries alone. There is an urgent need to better improve the control and eradication or elimination efforts towards NTDs. This can be achieved by utilizing machine learning tools to better the surveillance, prediction and detection program, and combat NTDs through the discovery of new therapeutics against these pathogens. This review surveys the current application of machine learning tools for NTDs and the challenges to elevate the state-of-the-art of NTDs surveillance, management, and treatment.
The Shapley value (SV) is adopted in various scenarios in machine learning (ML), including data valuation, agent valuation, and feature attribution, as it satisfies their fairness requirements. However, as exact SVs are infeasible to compute in practice, SV estimates are approximated instead. This approximation step raises an important question: do the SV estimates preserve the fairness guarantees of exact SVs? We observe that the fairness guarantees of exact SVs are too restrictive for SV estimates. Thus, we generalise Shapley fairness to probably approximate Shapley fairness and propose fidelity score, a metric to measure the variation of SV estimates, that determines how probable the fairness guarantees hold. Our last theoretical contribution is a novel greedy active estimation (GAE) algorithm that will maximise the lowest fidelity score and achieve a better fairness guarantee than the de facto Monte-Carlo estimation. We empirically verify GAE outperforms several existing methods in guaranteeing fairness while remaining competitive in estimation accuracy in various ML scenarios using real-world datasets.
Communication enables agents to cooperate to achieve their goals. Learning when to communicate, i.e., sparse (in time) communication, and whom to message is particularly important when bandwidth is limited. Recent work in learning sparse individualized communication, however, suffers from high variance during training, where decreasing communication comes at the cost of decreased reward, particularly in cooperative tasks. We use the information bottleneck to reframe sparsity as a representation learning problem, which we show naturally enables lossless sparse communication at lower budgets than prior art. In this paper, we propose a method for true lossless sparsity in communication via Information Maximizing Gated Sparse Multi-Agent Communication (IMGS-MAC). Our model uses two individualized regularization objectives, an information maximization autoencoder and sparse communication loss, to create informative and sparse communication. We evaluate the learned communication `language' through direct causal analysis of messages in non-sparse runs to determine the range of lossless sparse budgets, which allow zero-shot sparsity, and the range of sparse budgets that will inquire a reward loss, which is minimized by our learned gating function with few-shot sparsity. To demonstrate the efficacy of our results, we experiment in cooperative multi-agent tasks where communication is essential for success. We evaluate our model with both continuous and discrete messages. We focus our analysis on a variety of ablations to show the effect of message representations, including their properties, and lossless performance of our model.
Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution through an accept/reject mechanism which compares summary statistics of real and simulated data. To obviate the need for summary statistics, we directly compare empirical distributions with a Kullback-Leibler (KL) divergence estimator obtained via contrastive learning. In particular, we blend flexible machine learning classifiers within ABC to automate fake/real data comparisons. We consider the traditional accept/reject kernel as well as an exponential weighting scheme which does not require the ABC acceptance threshold. Our theoretical results show that the rate at which our ABC posterior distributions concentrate around the true parameter depends on the estimation error of the classifier. We derive limiting posterior shape results and find that, with a properly scaled exponential kernel, asymptotic normality holds. We demonstrate the usefulness of our approach on simulated examples as well as real data in the context of stock volatility estimation.
We study differentially private (DP) stochastic optimization (SO) with loss functions whose worst-case Lipschitz parameter over all data points may be extremely large. To date, the vast majority of work on DP SO assumes that the loss is uniformly Lipschitz continuous over data (i.e. stochastic gradients are uniformly bounded over all data points). While this assumption is convenient, it often leads to pessimistic excess risk bounds. In many practical problems, the worst-case Lipschitz parameter of the loss over all data points may be extremely large due to outliers. In such cases, the error bounds for DP SO, which scale with the worst-case Lipschitz parameter of the loss, are vacuous. To address these limitations, this work provides near-optimal excess risk bounds that do not depend on the uniform Lipschitz parameter of the loss. Building on a recent line of work [WXDX20, KLZ22], we assume that stochastic gradients have bounded $k$-th order moments for some $k \geq 2$. Compared with works on uniformly Lipschitz DP SO, our excess risk scales with the $k$-th moment bound instead of the uniform Lipschitz parameter of the loss, allowing for significantly faster rates in the presence of outliers and/or heavy-tailed data. For convex and strongly convex loss functions, we provide the first asymptotically optimal excess risk bounds (up to a logarithmic factor). In contrast to [WXDX20, KLZ22], our bounds do not require the loss function to be differentiable/smooth. We also devise an accelerated algorithm for smooth losses that runs in linear time and has excess risk that is tight in certain practical parameter regimes. Additionally, our work is the first to address non-convex non-uniformly Lipschitz loss functions satisfying the Proximal-PL inequality; this covers some practical machine learning models. Our Proximal-PL algorithm has near-optimal excess risk.
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed (i.i.d.) and the mean value of loss function is used as the empirical risk by Law of Large Numbers (LLN). This is known as the Monte Carlo method. However, when LLN is not applicable, such as imbalanced data problems, empirical risk will cause overfitting and might decrease robustness and generalization ability. Inspired by the framework of nonlinear expectation theory, we substitute the mean value of loss function with the maximum value of subgroup mean loss. We call it nonlinear Monte Carlo method. In order to use numerical method of optimization, we linearize and smooth the functional of maximum empirical risk and get the descent direction via quadratic programming. With the proposed method, we achieve better performance than SOTA backbone models with less training steps, and more robustness for basic regression and imbalanced classification tasks.
In 1954, Alston S. Householder published Principles of Numerical Analysis, one of the first modern treatments on matrix decomposition that favored a (block) LU decomposition-the factorization of a matrix into the product of lower and upper triangular matrices. And now, matrix decomposition has become a core technology in machine learning, largely due to the development of the back propagation algorithm in fitting a neural network. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in numerical linear algebra and matrix analysis in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of the Euclidean space, Hermitian space, Hilbert space, and things in the complex domain. We refer the reader to literature in the field of linear algebra for a more detailed introduction to the related fields.
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence. We suspect this behavior is due to the suboptimal selection of negatives used for offering contrast to the positives. We counter this difficulty by taking inspiration from support vector machines (SVMs) to present max-margin contrastive learning (MMCL). Our approach selects negatives as the sparse support vectors obtained via a quadratic optimization problem, and contrastiveness is enforced by maximizing the decision margin. As SVM optimization can be computationally demanding, especially in an end-to-end setting, we present simplifications that alleviate the computational burden. We validate our approach on standard vision benchmark datasets, demonstrating better performance in unsupervised representation learning over state-of-the-art, while having better empirical convergence properties.
For deploying a deep learning model into production, it needs to be both accurate and compact to meet the latency and memory constraints. This usually results in a network that is deep (to ensure performance) and yet thin (to improve computational efficiency). In this paper, we propose an efficient method to train a deep thin network with a theoretic guarantee. Our method is motivated by model compression. It consists of three stages. In the first stage, we sufficiently widen the deep thin network and train it until convergence. In the second stage, we use this well-trained deep wide network to warm up (or initialize) the original deep thin network. This is achieved by letting the thin network imitate the immediate outputs of the wide network from layer to layer. In the last stage, we further fine tune this well initialized deep thin network. The theoretical guarantee is established by using mean field analysis, which shows the advantage of layerwise imitation over traditional training deep thin networks from scratch by backpropagation. We also conduct large-scale empirical experiments to validate our approach. By training with our method, ResNet50 can outperform ResNet101, and BERT_BASE can be comparable with BERT_LARGE, where both the latter models are trained via the standard training procedures as in the literature.
Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.
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