arXiv subjects
Publications and source records attributed to Daniel Hsu.
We introduce interactive structure discovery, a generic framework that encompasses many interactive learning settings, including active learning, top-k item identification, interactive drug discovery, and others. We adapt a recently developed active learning algorithm of Tosh and Dasgupta (2017) for interactive structure discovery, and show that the new algorithm can be made noise-tolerant and enjoys favorable query complexity bounds.
Contrastive learning is an approach to representation learning that utilizes naturally occurring similar and dissimilar pairs of data points to find useful embeddings of data. In the context of document classification under topic modeling assumptions, we prove that contrastive learning is capable of recovering a representation of documents that reveals their underlying topic posterior information to linear models. We apply this procedure in a semi-supervised setup and demonstrate empirically that linear classifiers with these representations perform well in document classification tasks with very few training examples.
We propose a new randomized ensemble technique with a provable security guarantee against black-box transfer attacks. Our proof constructs a new security problem for random binary classifiers which is easier to empirically verify and a reduction from the security of this new model to the security of the ensemble classifier. We provide experimental evidence of the security of our random binary classifiers, as well as empirical results of the adversarial accuracy of the overall ensemble to black-box attacks. Our construction crucially leverages hidden randomness in the multiclass-to-binary reduction.
We seek to align agent policy with human expert behavior in a reinforcement learning (RL) setting, without any prior knowledge about dynamics, reward function, and unsafe states. There is a human expert knowing the rewards and unsafe states based on his preference and objective, but querying that human expert is expensive. To address this challenge, we propose a new framework for imitation learning (IL) algorithm that actively and interactively learns a model of the user's reward function with efficient queries. We build an adversarial generative model of states and a successor feature (SR) model trained over transition experience collected by learning policy. Our method uses these models to select state-action pairs, asking the user to comment on the optimality or safety, and trains a adversarial neural network to predict the rewards. Different from previous papers, which are almost all based on uncertainty sampling, the key idea is to actively and efficiently select state-action pairs from both on-policy and off-policy experience, by discriminating the queried (expert) and unqueried (generated) data and maximizing the efficiency of value function learning. We call this method adversarial reward query with successor representation. We evaluate the proposed method with simulated human on a state-based 2D navigation task, robotic control tasks and the image-based video games, which have high-dimensional observation and complex state dynamics. The results show that the proposed method significantly outperforms uncertainty-based methods on learning reward models, achieving better query efficiency, where the adversarial discriminator can make the agent learn human behavior more efficiently and the SR can select states which have stronger impact on value function. Moreover, the proposed method can also learn to avoid unsafe states when training the reward model.
We study least squares linear regression over $N$ uncorrelated Gaussian features that are selected in order of decreasing variance. When the number of selected features $p$ is at most the sample size $n$, the estimator under consideration coincides with the principal component regression estimator; when $p>n$, the estimator is the least $\ell_2$ norm solution over the selected features. We give an average-case analysis of the out-of-sample prediction error as $p,n,N \to \infty$ with $p/N \to α$ and $n/N \to β$, for some constants $α\in [0,1]$ and $β\in (0,1)$. In this average-case setting, the prediction error exhibits a "double descent" shape as a function of $p$. We also establish conditions under which the minimum risk is achieved in the interpolating ($p>n$) regime.
In many review classification applications, a fine-grained analysis of the reviews is desirable, because different segments (e.g., sentences) of a review may focus on different aspects of the entity in question. However, training supervised models for segment-level classification requires segment labels, which may be more difficult or expensive to obtain than review labels. In this paper, we employ Multiple Instance Learning (MIL) and use only weak supervision in the form of a single label per review. First, we show that when inappropriate MIL aggregation functions are used, then MIL-based networks are outperformed by simpler baselines. Second, we propose a new aggregation function based on the sigmoid attention mechanism and show that our proposed model outperforms the state-of-the-art models for segment-level sentiment classification (by up to 9.8% in F1). Finally, we highlight the importance of fine-grained predictions in an important public-health application: finding actionable reports of foodborne illness. We show that our model achieves 48.6% higher recall compared to previous models, thus increasing the chance of identifying previously unknown foodborne outbreaks.
Breakthroughs in machine learning are rapidly changing science and society, yet our fundamental understanding of this technology has lagged far behind. Indeed, one of the central tenets of the field, the bias-variance trade-off, appears to be at odds with the observed behavior of methods used in the modern machine learning practice. The bias-variance trade-off implies that a model should balance under-fitting and over-fitting: rich enough to express underlying structure in data, simple enough to avoid fitting spurious patterns. However, in the modern practice, very rich models such as neural networks are trained to exactly fit (i.e., interpolate) the data. Classically, such models would be considered over-fit, and yet they often obtain high accuracy on test data. This apparent contradiction has raised questions about the mathematical foundations of machine learning and their relevance to practitioners. In this paper, we reconcile the classical understanding and the modern practice within a unified performance curve. This "double descent" curve subsumes the textbook U-shaped bias-variance trade-off curve by showing how increasing model capacity beyond the point of interpolation results in improved performance. We provide evidence for the existence and ubiquity of double descent for a wide spectrum of models and datasets, and we posit a mechanism for its emergence. This connection between the performance and the structure of machine learning models delineates the limits of classical analyses, and has implications for both the theory and practice of machine learning.
Companies increasingly expose machine learning (ML) models trained over sensitive user data to untrusted domains, such as end-user devices and wide-access model stores. We present Sage, a differentially private (DP) ML platform that bounds the cumulative leakage of training data through models. Sage builds upon the rich literature on DP ML algorithms and contributes pragmatic solutions to two of the most pressing systems challenges of global DP: running out of privacy budget and the privacy-utility tradeoff. To address the former, we develop block composition, a new privacy loss accounting method that leverages the growing database regime of ML workloads to keep training models endlessly on a sensitive data stream while enforcing a global DP guarantee for the stream. To address the latter, we develop privacy-adaptive training, a process that trains a model on growing amounts of data and/or with increasing privacy parameters until, with high probability, the model meets developer-configured quality criteria. They illustrate how a systems focus on characteristics of ML workloads enables pragmatic solutions that are not apparent when one focuses on individual algorithms, as most DP ML literature does.
User-generated reviews can be decomposed into fine-grained segments (e.g., sentences, clauses), each evaluating a different aspect of the principal entity (e.g., price, quality, appearance). Automatically detecting these aspects can be useful for both users and downstream opinion mining applications. Current supervised approaches for learning aspect classifiers require many fine-grained aspect labels, which are labor-intensive to obtain. And, unfortunately, unsupervised topic models often fail to capture the aspects of interest. In this work, we consider weakly supervised approaches for training aspect classifiers that only require the user to provide a small set of seed words (i.e., weakly positive indicators) for the aspects of interest. First, we show that current weakly supervised approaches do not effectively leverage the predictive power of seed words for aspect detection. Next, we propose a student-teacher approach that effectively leverages seed words in a bag-of-words classifier (teacher); in turn, we use the teacher to train a second model (student) that is potentially more powerful (e.g., a neural network that uses pre-trained word embeddings). Finally, we show that iterative co-training can be used to cope with noisy seed words, leading to both improved teacher and student models. Our proposed approach consistently outperforms previous weakly supervised approaches (by 14.1 absolute F1 points on average) in six different domains of product reviews and six multilingual datasets of restaurant reviews.
This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source randomness of the network is a continuous distribution (the "semi-discrete" setting), then the Wasserstein distance is realized by a deterministic optimal transport mapping; (b) given an optimal transport mapping between a generator network and a target distribution, the Wasserstein distance may be decreased via a regression between the generated data and the mapped target points. The procedure here therefore alternates these two steps, forming an optimal transport and regressing against it, gradually adjusting the generator network towards the target distribution. Mathematically, this approach is shown to minimize the Wasserstein distance to both the empirical target distribution, and also its underlying population counterpart. Empirically, good performance is demonstrated on the training and testing sets of the MNIST and Thin-8 data. The paper closes with a discussion of the unsuitability of the Wasserstein distance for certain tasks, as has been identified in prior work [Arora et al., 2017, Huang et al., 2017].
Adversarial examples that fool machine learning models, particularly deep neural networks, have been a topic of intense research interest, with attacks and defenses being developed in a tight back-and-forth. Most past defenses are best effort and have been shown to be vulnerable to sophisticated attacks. Recently a set of certified defenses have been introduced, which provide guarantees of robustness to norm-bounded attacks, but they either do not scale to large datasets or are limited in the types of models they can support. This paper presents the first certified defense that both scales to large networks and datasets (such as Google's Inception network for ImageNet) and applies broadly to arbitrary model types. Our defense, called PixelDP, is based on a novel connection between robustness against adversarial examples and differential privacy, a cryptographically-inspired formalism, that provides a rigorous, generic, and flexible foundation for defense.
We present a method for predicting the space group of a structure given a calculated or measured atomic pair distribution function (PDF) from that structure. The method utilizes machine learning models trained on more than 100,000 PDFs calculated from structures in the 45 most heavily represented space groups. In particular, we present a convolutional neural network (CNN) model which yields a promising result that it correctly identifies the space group among the top-6 estimates 91.9~\% of the time. The CNN model also successfully identifies space groups on 12 out of 15 experimental PDFs. We discuss interesting aspects of the failed estimates, which indicate that the CNN is failing in similar ways as conventional indexing algorithms applied to conventional powder diffraction data. This preliminary success of the CNN model shows the possibility of model-independent assessment of PDF data on a wide class of materials.
Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, EUCLID, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher-order statistics such as the three-point correlation function, peak counts or Minkowski-functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2 or 3-dimensional astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of ($σ_8, Ω_m$) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4-2.8 times smaller credible contours than the power spectrum, and 3.5-4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4-2.1 times smaller contours than peak counts, a higher-order statistic capable of extracting non-Gaussian information from weak lensing maps.
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated classifiers appears to be ubiquitous in high-dimensional data, having been observed in deep networks, kernel machines, boosting and random forests. Their performance is consistently robust even when the data contain large amounts of label noise. Very little theory is available to explain these observations. The vast majority of theoretical analyses of generalization allows for interpolation only when there is little or no label noise. This paper takes a step toward a theoretical foundation for interpolated classifiers by analyzing local interpolating schemes, including geometric simplicial interpolation algorithm and singularly weighted $k$-nearest neighbor schemes. Consistency or near-consistency is proved for these schemes in classification and regression problems. Moreover, the nearest neighbor schemes exhibit optimal rates under some standard statistical assumptions. Finally, this paper suggests a way to explain the phenomenon of adversarial examples, which are seemingly ubiquitous in modern machine learning, and also discusses some connections to kernel machines and random forests in the interpolated regime.
Expectation Maximization (EM) is among the most popular algorithms for maximum likelihood estimation, but it is generally only guaranteed to find its stationary points of the log-likelihood objective. The goal of this article is to present theoretical and empirical evidence that over-parameterization can help EM avoid spurious local optima in the log-likelihood. We consider the problem of estimating the mean vectors of a Gaussian mixture model in a scenario where the mixing weights are known. Our study shows that the global behavior of EM, when one uses an over-parameterized model in which the mixing weights are treated as unknown, is better than that when one uses the (correct) model with the mixing weights fixed to the known values. For symmetric Gaussians mixtures with two components, we prove that introducing the (statistically redundant) weight parameters enables EM to find the global maximizer of the log-likelihood starting from almost any initial mean parameters, whereas EM without this over-parameterization may very often fail. For other Gaussian mixtures, we provide empirical evidence that shows similar behavior. Our results corroborate the value of over-parameterization in solving non-convex optimization problems, previously observed in other domains.
In this paper, we use augmented the hierarchical latent variable model to model multi-period time series, where the dynamics of time series are governed by factors or trends in multiple periods. Previous methods based on stacked recurrent neural network (RNN) and deep belief network (DBN) models cannot model the tendencies in multiple periods, and no models for sequential data pay special attention to redundant input variables which have no or even negative impact on prediction and modeling. Applying hierarchical latent variable model with multiple transition periods, our proposed algorithm can capture dependencies in different temporal resolutions. Introducing Bayesian neural network with Horseshoe prior as input network, we can discard the redundant input variables in the optimization process, concurrently with the learning of other parts of the model. Based on experiments with both synthetic and real-world data, we show that the proposed method significantly improves the modeling and prediction performance on multi-period time series.
Consider linear regression where the examples are generated by an unknown distribution on $R^d\times R$. Without any assumptions on the noise, the linear least squares solution for any i.i.d. sample will typically be biased w.r.t. the least squares optimum over the entire distribution. However, we show that if an i.i.d. sample of any size k is augmented by a certain small additional sample, then the solution of the combined sample becomes unbiased. We show this when the additional sample consists of d points drawn jointly according to the input distribution that is rescaled by the squared volume spanned by the points. Furthermore, we propose algorithms to sample from this volume-rescaled distribution when the data distribution is only known through an i.i.d sample.
Suppose an $n \times d$ design matrix in a linear regression problem is given, but the response for each point is hidden unless explicitly requested. The goal is to sample only a small number $k \ll n$ of the responses, and then produce a weight vector whose sum of squares loss over all points is at most $1+ε$ times the minimum. When $k$ is very small (e.g., $k=d$), jointly sampling diverse subsets of points is crucial. One such method called volume sampling has a unique and desirable property that the weight vector it produces is an unbiased estimate of the optimum. It is therefore natural to ask if this method offers the optimal unbiased estimate in terms of the number of responses $k$ needed to achieve a $1+ε$ loss approximation. Surprisingly we show that volume sampling can have poor behavior when we require a very accurate approximation -- indeed worse than some i.i.d. sampling techniques whose estimates are biased, such as leverage score sampling. We then develop a new rescaled variant of volume sampling that produces an unbiased estimate which avoids this bad behavior and has at least as good a tail bound as leverage score sampling: sample size $k=O(d\log d + d/ε)$ suffices to guarantee total loss at most $1+ε$ times the minimum with high probability. Thus, we improve on the best previously known sample size for an unbiased estimator, $k=O(d^2/ε)$. Our rescaling procedure leads to a new efficient algorithm for volume sampling which is based on a determinantal rejection sampling technique with potentially broader applications to determinantal point processes. Other contributions include introducing the combinatorics needed for rescaled volume sampling and developing tail bounds for sums of dependent random matrices which arise in the process.