Variational Inference with Holder Bounds

The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI). In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field. In particular, we elucidate how the TVO naturally connects the three key variational schemes, namely the importance-weighted VI, Renyi-VI, and MCMC-VI, which subsumes most VI objectives employed in practice. To explain the performance gap between theory and practice, we reveal how the pathological geometry of thermodynamic curves negatively affects TVO. By generalizing the integration path from the geometric mean to the weighted Holder mean, we extend the theory of TVO and identify new opportunities for improving VI. This motivates our new VI objectives, named the Holder bounds, which flatten the thermodynamic curves and promise to achieve a one-step approximation of the exact marginal log-likelihood. A comprehensive discussion on the choices of numerical estimators is provided. We present strong empirical evidence on both synthetic and real-world datasets to support our claims.

Finite-Time Consensus Learning for Decentralized Optimization with Nonlinear Gossiping

Distributed learning has become an integral tool for scaling up machine learning and addressing the growing need for data privacy. Although more robust to the network topology, decentralized learning schemes have not gained the same level of popularity as their centralized counterparts for being less competitive performance-wise. In this work, we attribute this issue to the lack of synchronization among decentralized learning workers, showing both empirically and theoretically that the convergence rate is tied to the synchronization level among the workers. Such motivated, we present a novel decentralized learning framework based on nonlinear gossiping (NGO), that enjoys an appealing finite-time consensus property to achieve better synchronization. We provide a careful analysis of its convergence and discuss its merits for modern distributed optimization applications, such as deep neural networks. Our analysis on how communication delay and randomized chats affect learning further enables the derivation of practical variants that accommodate asynchronous and randomized communications. To validate the effectiveness of our proposal, we benchmark NGO against competing solutions through an extensive set of tests, with encouraging results reported.

Hölder Bounds for Sensitivity Analysis in Causal Reasoning

We examine interval estimation of the effect of a treatment T on an outcome Y given the existence of an unobserved confounder U. Using H\"older's inequality, we derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding (i.e., the strength of the connection U->T, and the strength of U->Y). These bounds are tight either when U is independent of T or when U is independent of Y given T (when there is no unobserved confounding). We focus on a special case of this bound depending on the total variation distance between the distributions p(U) and p(U|T=t), as well as the maximum (over all possible values of U) deviation of the conditional expected outcome E[Y|U=u,T=t] from the average expected outcome E[Y|T=t]. We discuss possible calibration strategies for this bound to get interval estimates for treatment effects, and experimentally validate the bound using synthetic and semi-synthetic datasets.

Imputation-Free Learning from Incomplete Observations

Although recent works have developed methods that can generate estimations (or imputations) of the missing entries in a dataset to facilitate downstream analysis, most depend on assumptions that may not align with real-world applications and could suffer from poor performance in subsequent tasks. This is particularly true if the data have large missingness rates or a small population. More importantly, the imputation error could be propagated into the prediction step that follows, causing the gradients used to train the prediction models to be biased. Consequently, in this work, we introduce the importance guided stochastic gradient descent (IGSGD) method to train multilayer perceptrons (MLPs) and long short-term memories (LSTMs) to directly perform inference from inputs containing missing values without imputation. Specifically, we employ reinforcement learning (RL) to adjust the gradients used to train the models via back-propagation. This not only reduces bias but allows the model to exploit the underlying information behind missingness patterns. We test the proposed approach on real-world time-series (i.e., MIMIC-III), tabular data obtained from an eye clinic, and a standard dataset (i.e., MNIST), where our imputation-free predictions outperform the traditional two-step imputation-based predictions using state-of-the-art imputation methods.

Simpler, Faster, Stronger: Breaking The log-K Curse On Contrastive Learners With FlatNCE

InfoNCE-based contrastive representation learners, such as SimCLR, have been tremendously successful in recent years. However, these contrastive schemes are notoriously resource demanding, as their effectiveness breaks down with small-batch training (i.e., the log-K curse, whereas K is the batch-size). In this work, we reveal mathematically why contrastive learners fail in the small-batch-size regime, and present a novel simple, non-trivial contrastive objective named FlatNCE, which fixes this issue. Unlike InfoNCE, our FlatNCE no longer explicitly appeals to a discriminative classification goal for contrastive learning. Theoretically, we show FlatNCE is the mathematical dual formulation of InfoNCE, thus bridging the classical literature on energy modeling; and empirically, we demonstrate that, with minimal modification of code, FlatNCE enables immediate performance boost independent of the subject-matter engineering efforts. The significance of this work is furthered by the powerful generalization of contrastive learning techniques, and the introduction of new tools to monitor and diagnose contrastive training. We substantiate our claims with empirical evidence on CIFAR10, ImageNet, and other datasets, where FlatNCE consistently outperforms InfoNCE.

Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimization

Successful applications of InfoNCE and its variants have popularized the use of contrastive variational mutual information (MI) estimators in machine learning. While featuring superior stability, these estimators crucially depend on costly large-batch training, and they sacrifice bound tightness for variance reduction. To overcome these limitations, we revisit the mathematics of popular variational MI bounds from the lens of unnormalized statistical modeling and convex optimization. Our investigation not only yields a new unified theoretical framework encompassing popular variational MI bounds but also leads to a novel, simple, and powerful contrastive MI estimator named as FLO. Theoretically, we show that the FLO estimator is tight, and it provably converges under stochastic gradient descent. Empirically, our FLO estimator overcomes the limitations of its predecessors and learns more efficiently. The utility of FLO is verified using an extensive set of benchmarks, which also reveals the trade-offs in practical MI estimation.

Towards Fair Federated Learning with Zero-Shot Data Augmentation

Federated learning has emerged as an important distributed learning paradigm, where a server aggregates a global model from many client-trained models while having no access to the client data. Although it is recognized that statistical heterogeneity of the client local data yields slower global model convergence, it is less commonly recognized that it also yields a biased federated global model with a high variance of accuracy across clients. In this work, we aim to provide federated learning schemes with improved fairness. To tackle this challenge, we propose a novel federated learning system that employs zero-shot data augmentation on under-represented data to mitigate statistical heterogeneity and encourage more uniform accuracy performance across clients in federated networks. We study two variants of this scheme, Fed-ZDAC (federated learning with zero-shot data augmentation at the clients) and Fed-ZDAS (federated learning with zero-shot data augmentation at the server). Empirical results on a suite of datasets demonstrate the effectiveness of our methods on simultaneously improving the test accuracy and fairness.

Malignancy Prediction and Lesion Identification from Clinical Dermatological Images

We consider machine-learning-based malignancy prediction and lesion identification from clinical dermatological images, which can be indistinctly acquired via smartphone or dermoscopy capture. Additionally, we do not assume that images contain single lesions, thus the framework supports both focal or wide-field images. Specifically, we propose a two-stage approach in which we first identify all lesions present in the image regardless of sub-type or likelihood of malignancy, then it estimates their likelihood of malignancy, and through aggregation, it also generates an image-level likelihood of malignancy that can be used for high-level screening processes. Further, we consider augmenting the proposed approach with clinical covariates (from electronic health records) and publicly available data (the ISIC dataset). Comprehensive experiments validated on an independent test dataset demonstrate that i) the proposed approach outperforms alternative model architectures; ii) the model based on images outperforms a pure clinical model by a large margin, and the combination of images and clinical data does not significantly improves over the image-only model; and iii) the proposed framework offers comparable performance in terms of malignancy classification relative to three board certified dermatologists with different levels of experience.

Efficient Feature Transformations for Discriminative and Generative Continual Learning

As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown promise by naturally adding model capacity for learning new tasks while simultaneously avoiding catastrophic forgetting. However, the growth in the number of additional parameters of many of these types of methods can be computationally expensive at larger scales, at times prohibitively so. Instead, we propose a simple task-specific feature map transformation strategy for continual learning, which we call Efficient Feature Transformations (EFTs). These EFTs provide powerful flexibility for learning new tasks, achieved with minimal parameters added to the base architecture. We further propose a feature distance maximization strategy, which significantly improves task prediction in class incremental settings, without needing expensive generative models. We demonstrate the efficacy and efficiency of our method with an extensive set of experiments in discriminative (CIFAR-100 and ImageNet-1K) and generative (LSUN, CUB-200, Cats) sequences of tasks. Even with low single-digit parameter growth rates, EFTs can outperform many other continual learning methods in a wide range of settings.