arXiv subjects

Stefano Ermon

Publications and source records attributed to Stefano Ermon.

At least 199 records · Page 11Linked to original sources

arXiv2021

A Unified Framework for Multi-distribution Density Ratio Estimation

Binary density ratio estimation (DRE), the problem of estimating the ratio $p_1/p_2$ given their empirical samples, provides the foundation for many state-of-the-art machine learning algorithms such as contrastive representation learning and covariate shift adaptation. In this work, we consider a generalized setting where given samples from multiple distributions $p_1, \ldots, p_k$ (for $k > 2$), we aim to efficiently estimate the density ratios between all pairs of distributions. Such a generalization leads to important new applications such as estimating statistical discrepancy among multiple random variables like multi-distribution $f$-divergence, and bias correction via multiple importance sampling. We then develop a general framework from the perspective of Bregman divergence minimization, where each strictly convex multivariate function induces a proper loss for multi-distribution DRE. Moreover, we rederive the theoretical connection between multi-distribution density ratio estimation and class probability estimation, justifying the use of any strictly proper scoring rule composite with a link function for multi-distribution DRE. We show that our framework leads to methods that strictly generalize their counterparts in binary DRE, as well as new methods that show comparable or superior performance on various downstream tasks.

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arXiv2021

BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery

A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from observational data. However, a point estimate may not accurately capture the uncertainty in inferring the underlying graph in practical scenarios, wherein the true DAG is non-identifiable and/or the observed dataset is limited. We propose Bayesian Causal Discovery Nets (BCD Nets), a variational inference framework for estimating a distribution over DAGs characterizing a linear-Gaussian SEM. Developing a full Bayesian posterior over DAGs is challenging due to the the discrete and combinatorial nature of graphs. We analyse key design choices for scalable VI over DAGs, such as 1) the parametrization of DAGs via an expressive variational family, 2) a continuous relaxation that enables low-variance stochastic optimization, and 3) suitable priors over the latent variables. We provide a series of experiments on real and synthetic data showing that BCD Nets outperform maximum-likelihood methods on standard causal discovery metrics such as structural Hamming distance in low data regimes.

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arXiv2021

HyperSPNs: Compact and Expressive Probabilistic Circuits

Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for discrete density estimation tasks. However, large PCs are susceptible to overfitting, and only a few regularization strategies (e.g., dropout, weight-decay) have been explored. We propose HyperSPNs: a new paradigm of generating the mixture weights of large PCs using a small-scale neural network. Our framework can be viewed as a soft weight-sharing strategy, which combines the greater expressiveness of large models with the better generalization and memory-footprint properties of small models. We show the merits of our regularization strategy on two state-of-the-art PC families introduced in recent literature -- RAT-SPNs and EiNETs -- and demonstrate generalization improvements in both models on a suite of density estimation benchmarks in both discrete and continuous domains.

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arXiv2021

PiRank: Scalable Learning To Rank via Differentiable Sorting

A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w.r.t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof, and often fail to scale to real-world applications. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continuous, temperature-controlled relaxation to the sorting operator based on NeuralSort [1]. We show that PiRank exactly recovers the desired metrics in the limit of zero temperature and further propose a divide and-conquer extension that scales favorably to large list sizes, both in theory and practice. Empirically, we demonstrate the role of larger list sizes during training and show that PiRank significantly improves over comparable approaches on publicly available internet-scale learning-to-rank benchmarks.

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arXiv2021

Efficient Conditional Pre-training for Transfer Learning

Almost all the state-of-the-art neural networks for computer vision tasks are trained by (1) pre-training on a large-scale dataset and (2) finetuning on the target dataset. This strategy helps reduce dependence on the target dataset and improves convergence rate and generalization on the target task. Although pre-training on large-scale datasets is very useful, its foremost disadvantage is high training cost. To address this, we propose efficient filtering methods to select relevant subsets from the pre-training dataset. Additionally, we discover that lowering image resolutions in the pre-training step offers a great trade-off between cost and performance. We validate our techniques by pre-training on ImageNet in both the unsupervised and supervised settings and finetuning on a diverse collection of target datasets and tasks. Our proposed methods drastically reduce pre-training cost and provide strong performance boosts. Finally, we improve standard ImageNet pre-training by 1-3% by tuning available models on our subsets and pre-training on a dataset filtered from a larger scale dataset.

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arXiv2021

SustainBench: Benchmarks for Monitoring the Sustainable Development Goals with Machine Learning

Progress toward the United Nations Sustainable Development Goals (SDGs) has been hindered by a lack of data on key environmental and socioeconomic indicators, which historically have come from ground surveys with sparse temporal and spatial coverage. Recent advances in machine learning have made it possible to utilize abundant, frequently-updated, and globally available data, such as from satellites or social media, to provide insights into progress toward SDGs. Despite promising early results, approaches to using such data for SDG measurement thus far have largely evaluated on different datasets or used inconsistent evaluation metrics, making it hard to understand whether performance is improving and where additional research would be most fruitful. Furthermore, processing satellite and ground survey data requires domain knowledge that many in the machine learning community lack. In this paper, we introduce SustainBench, a collection of 15 benchmark tasks across 7 SDGs, including tasks related to economic development, agriculture, health, education, water and sanitation, climate action, and life on land. Datasets for 11 of the 15 tasks are released publicly for the first time. Our goals for SustainBench are to (1) lower the barriers to entry for the machine learning community to contribute to measuring and achieving the SDGs; (2) provide standard benchmarks for evaluating machine learning models on tasks across a variety of SDGs; and (3) encourage the development of novel machine learning methods where improved model performance facilitates progress towards the SDGs.

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arXiv2021

Estimating High Order Gradients of the Data Distribution by Denoising

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives provide additional local information about the data distribution and enable new applications. Although they can be estimated via automatic differentiation of a learned density model, this can amplify estimation errors and is expensive in high dimensional settings. To overcome these limitations, we propose a method to directly estimate high order derivatives (scores) of a data density from samples. We first show that denoising score matching can be interpreted as a particular case of Tweedie's formula. By leveraging Tweedie's formula on higher order moments, we generalize denoising score matching to estimate higher order derivatives. We demonstrate empirically that models trained with the proposed method can approximate second order derivatives more efficiently and accurately than via automatic differentiation. We show that our models can be used to quantify uncertainty in denoising and to improve the mixing speed of Langevin dynamics via Ozaki discretization for sampling synthetic data and natural images.

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arXiv2021

Pseudo-Spherical Contrastive Divergence

Energy-based models (EBMs) offer flexible distribution parametrization. However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum likelihood learning of EBMs. PS-CD is derived from the maximization of a family of strictly proper homogeneous scoring rules, which avoids the computation of the intractable partition function and provides a generalized family of learning objectives that include contrastive divergence as a special case. Moreover, PS-CD allows us to flexibly choose various learning objectives to train EBMs without additional computational cost or variational minimax optimization. Theoretical analysis on the proposed method and extensive experiments on both synthetic data and commonly used image datasets demonstrate the effectiveness and modeling flexibility of PS-CD, as well as its robustness to data contamination, thus showing its superiority over maximum likelihood and $f$-EBMs.

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arXiv2021

CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation

The imputation of missing values in time series has many applications in healthcare and finance. While autoregressive models are natural candidates for time series imputation, score-based diffusion models have recently outperformed existing counterparts including autoregressive models in many tasks such as image generation and audio synthesis, and would be promising for time series imputation. In this paper, we propose Conditional Score-based Diffusion models for Imputation (CSDI), a novel time series imputation method that utilizes score-based diffusion models conditioned on observed data. Unlike existing score-based approaches, the conditional diffusion model is explicitly trained for imputation and can exploit correlations between observed values. On healthcare and environmental data, CSDI improves by 40-65% over existing probabilistic imputation methods on popular performance metrics. In addition, deterministic imputation by CSDI reduces the error by 5-20% compared to the state-of-the-art deterministic imputation methods. Furthermore, CSDI can also be applied to time series interpolation and probabilistic forecasting, and is competitive with existing baselines. The code is available at https://github.com/ermongroup/CSDI.

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arXiv2021

Improving Compositionality of Neural Networks by Decoding Representations to Inputs

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated strong performance on novel applications, they sacrifice many of the functionalities of traditional software programs. With this as motivation, we take a modest first step towards improving deep learning programs by jointly training a generative model to constrain neural network activations to "decode" back to inputs. We call this design a Decodable Neural Network, or DecNN. Doing so enables a form of compositionality in neural networks, where one can recursively compose DecNN with itself to create an ensemble-like model with uncertainty. In our experiments, we demonstrate applications of this uncertainty to out-of-distribution detection, adversarial example detection, and calibration -- while matching standard neural networks in accuracy. We further explore this compositionality by combining DecNN with pretrained models, where we show promising results that neural networks can be regularized from using protected features.

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arXiv2021

Maximum Likelihood Training of Score-Based Diffusion Models

Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models can be tractably computed through a connection to continuous normalizing flows, but log-likelihood is not directly optimized by the weighted combination of score matching losses. We show that for a specific weighting scheme, the objective upper bounds the negative log-likelihood, thus enabling approximate maximum likelihood training of score-based diffusion models. We empirically observe that maximum likelihood training consistently improves the likelihood of score-based diffusion models across multiple datasets, stochastic processes, and model architectures. Our best models achieve negative log-likelihoods of 2.83 and 3.76 bits/dim on CIFAR-10 and ImageNet 32x32 without any data augmentation, on a par with state-of-the-art autoregressive models on these tasks.

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arXiv2021

Equivariant Neural Network for Factor Graphs

Several indices used in a factor graph data structure can be permuted without changing the underlying probability distribution. An algorithm that performs inference on a factor graph should ideally be equivariant or invariant to permutations of global indices of nodes, variable orderings within a factor, and variable assignment orderings. However, existing neural network-based inference procedures fail to take advantage of this inductive bias. In this paper, we precisely characterize these isomorphic properties of factor graphs and propose two inference models: Factor-Equivariant Neural Belief Propagation (FE-NBP) and Factor-Equivariant Graph Neural Networks (FE-GNN). FE-NBP is a neural network that generalizes BP and respects each of the above properties of factor graphs while FE-GNN is an expressive GNN model that relaxes an isomorphic property in favor of greater expressivity. Empirically, we demonstrate on both real-world and synthetic datasets, for both marginal inference and MAP inference, that FE-NBP and FE-GNN together cover a range of sample complexity regimes: FE-NBP achieves state-of-the-art performance on small datasets while FE-GNN achieves state-of-the-art performance on large datasets.

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arXiv2021

Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration

When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated -- amongst the inputs that receive a predicted class probabilities vector $q$, the actual distribution over classes is $q$. For multi-class prediction problems, however, achieving distribution calibration tends to be infeasible, requiring sample complexity exponential in the number of classes $C$. In this work, we introduce a new notion -- \emph{decision calibration} -- that requires the predicted distribution and true distribution to be ``indistinguishable'' to a set of downstream decision-makers. When all possible decision makers are under consideration, decision calibration is the same as distribution calibration. However, when we only consider decision makers choosing between a bounded number of actions (e.g. polynomial in $C$), our main result shows that decisions calibration becomes feasible -- we design a recalibration algorithm that requires sample complexity polynomial in the number of actions and the number of classes. We validate our recalibration algorithm empirically: compared to existing methods, decision calibration improves decision-making on skin lesion and ImageNet classification with modern neural network predictors.

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arXiv2021

Multi-Agent Imitation Learning with Copulas

Multi-agent imitation learning aims to train multiple agents to perform tasks from demonstrations by learning a mapping between observations and actions, which is essential for understanding physical, social, and team-play systems. However, most existing works on modeling multi-agent interactions typically assume that agents make independent decisions based on their observations, ignoring the complex dependence among agents. In this paper, we propose to use copula, a powerful statistical tool for capturing dependence among random variables, to explicitly model the correlation and coordination in multi-agent systems. Our proposed model is able to separately learn marginals that capture the local behavioral patterns of each individual agent, as well as a copula function that solely and fully captures the dependence structure among agents. Extensive experiments on synthetic and real-world datasets show that our model outperforms state-of-the-art baselines across various scenarios in the action prediction task, and is able to generate new trajectories close to expert demonstrations.

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arXiv2021

Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Information

In many real-world problems, we want to infer some property of an expensive black-box function $f$, given a budget of $T$ function evaluations. One example is budget constrained global optimization of $f$, for which Bayesian optimization is a popular method. Other properties of interest include local optima, level sets, integrals, or graph-structured information induced by $f$. Often, we can find an algorithm $\mathcal{A}$ to compute the desired property, but it may require far more than $T$ queries to execute. Given such an $\mathcal{A}$, and a prior distribution over $f$, we refer to the problem of inferring the output of $\mathcal{A}$ using $T$ evaluations as Bayesian Algorithm Execution (BAX). To tackle this problem, we present a procedure, InfoBAX, that sequentially chooses queries that maximize mutual information with respect to the algorithm's output. Applying this to Dijkstra's algorithm, for instance, we infer shortest paths in synthetic and real-world graphs with black-box edge costs. Using evolution strategies, we yield variants of Bayesian optimization that target local, rather than global, optima. On these problems, InfoBAX uses up to 500 times fewer queries to $f$ than required by the original algorithm. Our method is closely connected to other Bayesian optimal experimental design procedures such as entropy search methods and optimal sensor placement using Gaussian processes.

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arXiv2021

Featurized Density Ratio Estimation

Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are sufficiently different. In our work, we propose to leverage an invertible generative model to map the two distributions into a common feature space prior to estimation. This featurization brings the densities closer together in latent space, sidestepping pathological scenarios where the learned density ratios in input space can be arbitrarily inaccurate. At the same time, the invertibility of our feature map guarantees that the ratios computed in feature space are equivalent to those in input space. Empirically, we demonstrate the efficacy of our approach in a variety of downstream tasks that require access to accurate density ratios such as mutual information estimation, targeted sampling in deep generative models, and classification with data augmentation.

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arXiv2021

Temporal Predictive Coding For Model-Based Planning In Latent Space

High-dimensional observations are a major challenge in the application of model-based reinforcement learning (MBRL) to real-world environments. To handle high-dimensional sensory inputs, existing approaches use representation learning to map high-dimensional observations into a lower-dimensional latent space that is more amenable to dynamics estimation and planning. In this work, we present an information-theoretic approach that employs temporal predictive coding to encode elements in the environment that can be predicted across time. Since this approach focuses on encoding temporally-predictable information, we implicitly prioritize the encoding of task-relevant components over nuisance information within the environment that are provably task-irrelevant. By learning this representation in conjunction with a recurrent state space model, we can then perform planning in latent space. We evaluate our model on a challenging modification of standard DMControl tasks where the background is replaced with natural videos that contain complex but irrelevant information to the planning task. Our experiments show that our model is superior to existing methods in the challenging complex-background setting while remaining competitive with current state-of-the-art models in the standard setting.

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arXiv2021

D2C: Diffusion-Denoising Models for Few-shot Conditional Generation

Conditional generative models of high-dimensional images have many applications, but supervision signals from conditions to images can be expensive to acquire. This paper describes Diffusion-Decoding models with Contrastive representations (D2C), a paradigm for training unconditional variational autoencoders (VAEs) for few-shot conditional image generation. D2C uses a learned diffusion-based prior over the latent representations to improve generation and contrastive self-supervised learning to improve representation quality. D2C can adapt to novel generation tasks conditioned on labels or manipulation constraints, by learning from as few as 100 labeled examples. On conditional generation from new labels, D2C achieves superior performance over state-of-the-art VAEs and diffusion models. On conditional image manipulation, D2C generations are two orders of magnitude faster to produce over StyleGAN2 ones and are preferred by 50% - 60% of the human evaluators in a double-blind study.

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