arXiv subjects

Pradeep Ravikumar

Publications and source records attributed to Pradeep Ravikumar.

At least 73 records · Page 4Linked to original sources

arXiv2021

Analyzing and Improving the Optimization Landscape of Noise-Contrastive Estimation

Noise-contrastive estimation (NCE) is a statistically consistent method for learning unnormalized probabilistic models. It has been empirically observed that the choice of the noise distribution is crucial for NCE's performance. However, such observations have never been made formal or quantitative. In fact, it is not even clear whether the difficulties arising from a poorly chosen noise distribution are statistical or algorithmic in nature. In this work, we formally pinpoint reasons for NCE's poor performance when an inappropriate noise distribution is used. Namely, we prove these challenges arise due to an ill-behaved (more precisely, flat) loss landscape. To address this, we introduce a variant of NCE called "eNCE" which uses an exponential loss and for which normalized gradient descent addresses the landscape issues provably when the target and noise distributions are in a given exponential family.

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arXiv2021

On Proximal Policy Optimization's Heavy-tailed Gradients

Modern policy gradient algorithms such as Proximal Policy Optimization (PPO) rely on an arsenal of heuristics, including loss clipping and gradient clipping, to ensure successful learning. These heuristics are reminiscent of techniques from robust statistics, commonly used for estimation in outlier-rich (``heavy-tailed'') regimes. In this paper, we present a detailed empirical study to characterize the heavy-tailed nature of the gradients of the PPO surrogate reward function. We demonstrate that the gradients, especially for the actor network, exhibit pronounced heavy-tailedness and that it increases as the agent's policy diverges from the behavioral policy (i.e., as the agent goes further off policy). Further examination implicates the likelihood ratios and advantages in the surrogate reward as the main sources of the observed heavy-tailedness. We then highlight issues arising due to the heavy-tailed nature of the gradients. In this light, we study the effects of the standard PPO clipping heuristics, demonstrating that these tricks primarily serve to offset heavy-tailedness in gradients. Thus motivated, we propose incorporating GMOM, a high-dimensional robust estimator, into PPO as a substitute for three clipping tricks. Despite requiring less hyperparameter tuning, our method matches the performance of PPO (with all heuristics enabled) on a battery of MuJoCo continuous control tasks.

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arXiv2021

Improving Compositional Generalization in Classification Tasks via Structure Annotations

Compositional generalization is the ability to generalize systematically to a new data distribution by combining known components. Although humans seem to have a great ability to generalize compositionally, state-of-the-art neural models struggle to do so. In this work, we study compositional generalization in classification tasks and present two main contributions. First, we study ways to convert a natural language sequence-to-sequence dataset to a classification dataset that also requires compositional generalization. Second, we show that providing structural hints (specifically, providing parse trees and entity links as attention masks for a Transformer model) helps compositional generalization.

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arXiv2021

DORO: Distributional and Outlier Robust Optimization

Many machine learning tasks involve subpopulation shift where the testing data distribution is a subpopulation of the training distribution. For such settings, a line of recent work has proposed the use of a variant of empirical risk minimization(ERM) known as distributionally robust optimization (DRO). In this work, we apply DRO to real, large-scale tasks with subpopulation shift, and observe that DRO performs relatively poorly, and moreover has severe instability. We identify one direct cause of this phenomenon: sensitivity of DRO to outliers in the datasets. To resolve this issue, we propose the framework of DORO, for Distributional and Outlier Robust Optimization. At the core of this approach is a refined risk function which prevents DRO from overfitting to potential outliers. We instantiate DORO for the Cressie-Read family of Rényi divergence, and delve into two specific instances of this family: CVaR and $χ^2$-DRO. We theoretically prove the effectiveness of the proposed method, and empirically show that DORO improves the performance and stability of DRO with experiments on large modern datasets, thereby positively addressing the open question raised by Hashimoto et al., 2018.

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arXiv2021

Evaluations and Methods for Explanation through Robustness Analysis

Feature based explanations, that provide importance of each feature towards the model prediction, is arguably one of the most intuitive ways to explain a model. In this paper, we establish a novel set of evaluation criteria for such feature based explanations by robustness analysis. In contrast to existing evaluations which require us to specify some way to "remove" features that could inevitably introduces biases and artifacts, we make use of the subtler notion of smaller adversarial perturbations. By optimizing towards our proposed evaluation criteria, we obtain new explanations that are loosely necessary and sufficient for a prediction. We further extend the explanation to extract the set of features that would move the current prediction to a target class by adopting targeted adversarial attack for the robustness analysis. Through experiments across multiple domains and a user study, we validate the usefulness of our evaluation criteria and our derived explanations.

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arXiv2021

The Risks of Invariant Risk Minimization

Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain constant. Recently, Arjovsky et al. (2019) proposed Invariant Risk Minimization (IRM), an objective based on this idea for learning deep, invariant features of data which are a complex function of latent variables; many alternatives have subsequently been suggested. However, formal guarantees for all of these works are severely lacking. In this paper, we present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model. In the linear case, we show simple conditions under which the optimal solution succeeds or, more often, fails to recover the optimal invariant predictor. We furthermore present the very first results in the non-linear regime: we demonstrate that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve. Thus, in this setting we find that IRM and its alternatives fundamentally do not improve over standard Empirical Risk Minimization.

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arXiv2021

Contrastive learning of strong-mixing continuous-time stochastic processes

Contrastive learning is a family of self-supervised methods where a model is trained to solve a classification task constructed from unlabeled data. It has recently emerged as one of the leading learning paradigms in the absence of labels across many different domains (e.g. brain imaging, text, images). However, theoretical understanding of many aspects of training, both statistical and algorithmic, remain fairly elusive. In this work, we study the setting of time series -- more precisely, when we get data from a strong-mixing continuous-time stochastic process. We show that a properly constructed contrastive learning task can be used to estimate the transition kernel for small-to-mid-range intervals in the diffusion case. Moreover, we give sample complexity bounds for solving this task and quantitatively characterize what the value of the contrastive loss implies for distributional closeness of the learned kernel. As a byproduct, we illuminate the appropriate settings for the contrastive distribution, as well as other hyperparameters in this setup.

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arXiv2020

Efficient Tensor Decomposition with Boolean Factors

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching Pursuit (BMP), a novel generalization of the matching pursuit strategy to decompose the tensor efficiently. BMP iteratively searches for atoms in a greedy fashion. The greedy atom search step is solved efficiently via a MAXCUT-like boolean quadratic program. We prove that BMP is guaranteed to converge sublinearly to the optimal solution and recover the factors under mild identifiability conditions. Experiments demonstrate the superior performance of our method over baselines on synthetic and real datasets. We also showcase the application of BMP in quantifying neural interactions underlying high-resolution spatiotemporal ECoG recordings.

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arXiv2020

Certified Robustness to Label-Flipping Attacks via Randomized Smoothing

Machine learning algorithms are known to be susceptible to data poisoning attacks, where an adversary manipulates the training data to degrade performance of the resulting classifier. In this work, we present a unifying view of randomized smoothing over arbitrary functions, and we leverage this novel characterization to propose a new strategy for building classifiers that are pointwise-certifiably robust to general data poisoning attacks. As a specific instantiation, we utilize our framework to build linear classifiers that are robust to a strong variant of label flipping, where each test example is targeted independently. In other words, for each test point, our classifier includes a certification that its prediction would be the same had some number of training labels been changed adversarially. Randomized smoothing has previously been used to guarantee---with high probability---test-time robustness to adversarial manipulation of the input to a classifier; we derive a variant which provides a deterministic, analytical bound, sidestepping the probabilistic certificates that traditionally result from the sampling subprocedure. Further, we obtain these certified bounds with minimal additional runtime complexity over standard classification and no assumptions on the train or test distributions. We generalize our results to the multi-class case, providing the first multi-class classification algorithm that is certifiably robust to label-flipping attacks.

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arXiv2020

Automated Dependence Plots

In practical applications of machine learning, it is necessary to look beyond standard metrics such as test accuracy in order to validate various qualitative properties of a model. Partial dependence plots (PDP), including instance-specific PDPs (i.e., ICE plots), have been widely used as a visual tool to understand or validate a model. Yet, current PDPs suffer from two main drawbacks: (1) a user must manually sort or select interesting plots, and (2) PDPs are usually limited to plots along a single feature. To address these drawbacks, we formalize a method for automating the selection of interesting PDPs and extend PDPs beyond showing single features to show the model response along arbitrary directions, for example in raw feature space or a latent space arising from some generative model. We demonstrate the usefulness of our automated dependence plots (ADP) across multiple use-cases and datasets including model selection, bias detection, understanding out-of-sample behavior, and exploring the latent space of a generative model.

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arXiv2020

Sharp Statistical Guarantees for Adversarially Robust Gaussian Classification

Adversarial robustness has become a fundamental requirement in modern machine learning applications. Yet, there has been surprisingly little statistical understanding so far. In this paper, we provide the first result of the optimal minimax guarantees for the excess risk for adversarially robust classification, under Gaussian mixture model proposed by \cite{schmidt2018adversarially}. The results are stated in terms of the Adversarial Signal-to-Noise Ratio (AdvSNR), which generalizes a similar notion for standard linear classification to the adversarial setting. For the Gaussian mixtures with AdvSNR value of $r$, we establish an excess risk lower bound of order $Θ(e^{-(\frac{1}{8}+o(1)) r^2} \frac{d}{n})$ and design a computationally efficient estimator that achieves this optimal rate. Our results built upon minimal set of assumptions while cover a wide spectrum of adversarial perturbations including $\ell_p$ balls for any $p \ge 1$.

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arXiv2020

Sub-Seasonal Climate Forecasting via Machine Learning: Challenges, Analysis, and Advances

Sub-seasonal climate forecasting (SSF) focuses on predicting key climate variables such as temperature and precipitation in the 2-week to 2-month time scales. Skillful SSF would have immense societal value, in areas such as agricultural productivity, water resource management, transportation and aviation systems, and emergency planning for extreme weather events. However, SSF is considered more challenging than either weather prediction or even seasonal prediction. In this paper, we carefully study a variety of machine learning (ML) approaches for SSF over the US mainland. While atmosphere-land-ocean couplings and the limited amount of good quality data makes it hard to apply black-box ML naively, we show that with carefully constructed feature representations, even linear regression models, e.g., Lasso, can be made to perform well. Among a broad suite of 10 ML approaches considered, gradient boosting performs the best, and deep learning (DL) methods show some promise with careful architecture choices. Overall, suitable ML methods are able to outperform the climatological baseline, i.e., predictions based on the 30-year average at a given location and time. Further, based on studying feature importance, ocean (especially indices based on climatic oscillations such as El Nino) and land (soil moisture) covariates are found to be predictive, whereas atmospheric covariates are not considered helpful.

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arXiv2020

Learning Minimax Estimators via Online Learning

We consider the problem of designing minimax estimators for estimating the parameters of a probability distribution. Unlike classical approaches such as the MLE and minimum distance estimators, we consider an algorithmic approach for constructing such estimators. We view the problem of designing minimax estimators as finding a mixed strategy Nash equilibrium of a zero-sum game. By leveraging recent results in online learning with non-convex losses, we provide a general algorithm for finding a mixed-strategy Nash equilibrium of general non-convex non-concave zero-sum games. Our algorithm requires access to two subroutines: (a) one which outputs a Bayes estimator corresponding to a given prior probability distribution, and (b) one which computes the worst-case risk of any given estimator. Given access to these two subroutines, we show that our algorithm outputs both a minimax estimator and a least favorable prior. To demonstrate the power of this approach, we use it to construct provably minimax estimators for classical problems such as estimation in the finite Gaussian sequence model, and linear regression.

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arXiv2020

Class-Weighted Classification: Trade-offs and Robust Approaches

We address imbalanced classification, the problem in which a label may have low marginal probability relative to other labels, by weighting losses according to the correct class. First, we examine the convergence rates of the expected excess weighted risk of plug-in classifiers where the weighting for the plug-in classifier and the risk may be different. This leads to irreducible errors that do not converge to the weighted Bayes risk, which motivates our consideration of robust risks. We define a robust risk that minimizes risk over a set of weightings and show excess risk bounds for this problem. Finally, we show that particular choices of the weighting set leads to a special instance of conditional value at risk (CVaR) from stochastic programming, which we call label conditional value at risk (LCVaR). Additionally, we generalize this weighting to derive a new robust risk problem that we call label heterogeneous conditional value at risk (LHCVaR). Finally, we empirically demonstrate the efficacy of LCVaR and LHCVaR on improving class conditional risks.

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arXiv2020

Minimizing FLOPs to Learn Efficient Sparse Representations

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

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arXiv2020

Learning Sparse Nonparametric DAGs

We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this algebraic characterization to nonparametric SEM by leveraging nonparametric sparsity based on partial derivatives, resulting in a continuous optimization problem that can be applied to a variety of nonparametric and semiparametric models including GLMs, additive noise models, and index models as special cases. Unlike existing approaches that require specific modeling choices, loss functions, or algorithms, we present a completely general framework that can be applied to general nonlinear models (e.g. without additive noise), general differentiable loss functions, and generic black-box optimization routines. The code is available at https://github.com/xunzheng/notears.

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arXiv2020

Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e. misspecified) mixture models. These identifiability conditions generalize existing conditions in the literature, and are flexible enough to include for example mixtures of Gaussian mixtures. In contrast to the recent literature on estimating nonparametric mixtures, we allow for general nonparametric mixture components, and instead impose regularity assumptions on the underlying mixing measure. As our primary application, we apply these results to partition-based clustering, generalizing the notion of a Bayes optimal partition from classical parametric model-based clustering to nonparametric settings. Furthermore, this framework is constructive so that it yields a practical algorithm for learning identified mixtures, which is illustrated through several examples on real data. The key conceptual device in the analysis is the convex, metric geometry of probability measures on metric spaces and its connection to the Wasserstein convergence of mixing measures. The result is a flexible framework for nonparametric clustering with formal consistency guarantees.

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arXiv2019

Game Design for Eliciting Distinguishable Behavior

The ability to inferring latent psychological traits from human behavior is key to developing personalized human-interacting machine learning systems. Approaches to infer such traits range from surveys to manually-constructed experiments and games. However, these traditional games are limited because they are typically designed based on heuristics. In this paper, we formulate the task of designing \emph{behavior diagnostic games} that elicit distinguishable behavior as a mutual information maximization problem, which can be solved by optimizing a variational lower bound. Our framework is instantiated by using prospect theory to model varying player traits, and Markov Decision Processes to parameterize the games. We validate our approach empirically, showing that our designed games can successfully distinguish among players with different traits, outperforming manually-designed ones by a large margin.

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