arXiv subjects

Daniel Hsu

Publications and source records attributed to Daniel Hsu.

At least 55 records · Page 3Linked to original sources

arXiv2022

Anomaly Detection on Graph Time Series

In this paper, we use variational recurrent neural network to investigate the anomaly detection problem on graph time series. The temporal correlation is modeled by the combination of recurrent neural network (RNN) and variational inference (VI), while the spatial information is captured by the graph convolutional network. In order to incorporate external factors, we use feature extractor to augment the transition of latent variables, which can learn the influence of external factors. With the target function as accumulative ELBO, it is easy to extend this model to on-line method. The experimental study on traffic flow data shows the detection capability of the proposed method.

cs.LG↗

arXiv2022

Masked prediction tasks: a parameter identifiability view

The vast majority of work in self-supervised learning, both theoretical and empirical (though mostly the latter), have largely focused on recovering good features for downstream tasks, with the definition of "good" often being intricately tied to the downstream task itself. This lens is undoubtedly very interesting, but suffers from the problem that there isn't a "canonical" set of downstream tasks to focus on -- in practice, this problem is usually resolved by competing on the benchmark dataset du jour. In this paper, we present an alternative lens: one of parameter identifiability. More precisely, we consider data coming from a parametric probabilistic model, and train a self-supervised learning predictor with a suitably chosen parametric form. Then, we ask whether we can read off the ground truth parameters of the probabilistic model from the optimal predictor. We focus on the widely used self-supervised learning method of predicting masked tokens, which is popular for both natural languages and visual data. While incarnations of this approach have already been successfully used for simpler probabilistic models (e.g. learning fully-observed undirected graphical models), we focus instead on latent-variable models capturing sequential structures -- namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We show that there is a rich landscape of possibilities, out of which some prediction tasks yield identifiability, while others do not. Our results, borne of a theoretical grounding of self-supervised learning, could thus potentially beneficially inform practice. Moreover, we uncover close connections with uniqueness of tensor rank decompositions -- a widely used tool in studying identifiability through the lens of the method of moments.

cs.LG↗

arXiv2022

Near-Optimal Statistical Query Lower Bounds for Agnostically Learning Intersections of Halfspaces with Gaussian Marginals

We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ) algorithm for agnostically learning the class of intersections of $k$ halfspaces over $\mathbb{R}^n$ to constant excess error either must make queries of tolerance at most $n^{-\tildeΩ(\sqrt{\log k})}$ or must make $2^{n^{Ω(1)}}$ queries. We strengthen this result by improving the tolerance requirement to $n^{-\tildeΩ(\log k)}$. This lower bound is essentially best possible since an SQ algorithm of Klivans et al. (2008) agnostically learns this class to any constant excess error using $n^{O(\log k)}$ queries of tolerance $n^{-O(\log k)}$. We prove two variants of our lower bound, each of which combines ingredients from Diakonikolas et al. (2021) with (an extension of) a different earlier approach for agnostic SQ lower bounds for the Boolean setting due to Dachman-Soled et al. (2014). Our approach also yields lower bounds for agnostically SQ learning the class of "convex subspace juntas" (studied by Vempala, 2010) and the class of sets with bounded Gaussian surface area; all of these lower bounds are nearly optimal since they essentially match known upper bounds from Klivans et al. (2008).

cs.LG↗

arXiv2022

Learning Tensor Representations for Meta-Learning

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different tasks, and do not consider the additional task-specific observable side information. In this work, we model the meta-parameter through an order-$3$ tensor, which can adapt to the observed task features of the task. We propose two methods to estimate the underlying tensor. The first method solves a tensor regression problem and works under natural assumptions on the data generating process. The second method uses the method of moments under additional distributional assumptions and has an improved sample complexity in terms of the number of tasks. We also focus on the meta-test phase, and consider estimating task-specific parameters on a new task. Substituting the estimated tensor from the first step allows us estimating the task-specific parameters with very few samples of the new task, thereby showing the benefits of learning tensor representations for meta-learning. Finally, through simulation and several real-world datasets, we evaluate our methods and show that it improves over previous linear models of shared representations for meta-learning.

cs.LG↗

arXiv2021

Support vector machines and linear regression coincide with very high-dimensional features

The support vector machine (SVM) and minimum Euclidean norm least squares regression are two fundamentally different approaches to fitting linear models, but they have recently been connected in models for very high-dimensional data through a phenomenon of support vector proliferation, where every training example used to fit an SVM becomes a support vector. In this paper, we explore the generality of this phenomenon and make the following contributions. First, we prove a super-linear lower bound on the dimension (in terms of sample size) required for support vector proliferation in independent feature models, matching the upper bounds from previous works. We further identify a sharp phase transition in Gaussian feature models, bound the width of this transition, and give experimental support for its universality. Finally, we hypothesize that this phase transition occurs only in much higher-dimensional settings in the $\ell_1$ variant of the SVM, and we present a new geometric characterization of the problem that may elucidate this phenomenon for the general $\ell_p$ case.

cs.LG↗

arXiv2021

Classification vs regression in overparameterized regimes: Does the loss function matter?

We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by least-squares minimum-norm interpolation, typically used for regression, are identical to those produced by the hard-margin support vector machine (SVM) that minimizes the hinge loss, typically used for training classifiers. On the other hand, we show that there exist regimes where these interpolating solutions generalize well when evaluated by the 0-1 test loss function, but do not generalize if evaluated by the square loss function, i.e. they approach the null risk. Our results demonstrate the very different roles and properties of loss functions used at the training phase (optimization) and the testing phase (generalization).

cs.LG↗

arXiv2021

On the Approximation Power of Two-Layer Networks of Random ReLUs

This paper considers the following question: how well can depth-two ReLU networks with randomly initialized bottom-level weights represent smooth functions? We give near-matching upper- and lower-bounds for $L_2$-approximation in terms of the Lipschitz constant, the desired accuracy, and the dimension of the problem, as well as similar results in terms of Sobolev norms. Our positive results employ tools from harmonic analysis and ridgelet representation theory, while our lower-bounds are based on (robust versions of) dimensionality arguments.

cs.LG↗

arXiv2021

Bayesian decision-making under misspecified priors with applications to meta-learning

Thompson sampling and other Bayesian sequential decision-making algorithms are among the most popular approaches to tackle explore/exploit trade-offs in (contextual) bandits. The choice of prior in these algorithms offers flexibility to encode domain knowledge but can also lead to poor performance when misspecified. In this paper, we demonstrate that performance degrades gracefully with misspecification. We prove that the expected reward accrued by Thompson sampling (TS) with a misspecified prior differs by at most $\tilde{\mathcal{O}}(H^2 ε)$ from TS with a well specified prior, where $ε$ is the total-variation distance between priors and $H$ is the learning horizon. Our bound does not require the prior to have any parametric form. For priors with bounded support, our bound is independent of the cardinality or structure of the action space, and we show that it is tight up to universal constants in the worst case. Building on our sensitivity analysis, we establish generic PAC guarantees for algorithms in the recently studied Bayesian meta-learning setting and derive corollaries for various families of priors. Our results generalize along two axes: (1) they apply to a broader family of Bayesian decision-making algorithms, including a Monte-Carlo implementation of the knowledge gradient algorithm (KG), and (2) they apply to Bayesian POMDPs, the most general Bayesian decision-making setting, encompassing contextual bandits as a special case. Through numerical simulations, we illustrate how prior misspecification and the deployment of one-step look-ahead (as in KG) can impact the convergence of meta-learning in multi-armed and contextual bandits with structured and correlated priors.

cs.LG↗

arXiv2021

Contrastive learning, multi-view redundancy, and linear models

Self-supervised learning is an empirically successful approach to unsupervised learning based on creating artificial supervised learning problems. A popular self-supervised approach to representation learning is contrastive learning, which leverages naturally occurring pairs of similar and dissimilar data points, or multiple views of the same data. This work provides a theoretical analysis of contrastive learning in the multi-view setting, where two views of each datum are available. The main result is that linear functions of the learned representations are nearly optimal on downstream prediction tasks whenever the two views provide redundant information about the label.

cs.LG↗

arXiv2021

Generalization bounds via distillation

This paper theoretically investigates the following empirical phenomenon: given a high-complexity network with poor generalization bounds, one can distill it into a network with nearly identical predictions but low complexity and vastly smaller generalization bounds. The main contribution is an analysis showing that the original network inherits this good generalization bound from its distillation, assuming the use of well-behaved data augmentation. This bound is presented both in an abstract and in a concrete form, the latter complemented by a reduction technique to handle modern computation graphs featuring convolutional layers, fully-connected layers, and skip connections, to name a few. To round out the story, a (looser) classical uniform convergence analysis of compression is also presented, as well as a variety of experiments on cifar and mnist demonstrating similar generalization performance between the original network and its distillation.

cs.LG↗

arXiv2021

Statistical Query Lower Bounds for Tensor PCA

In the Tensor PCA problem introduced by Richard and Montanari (2014), one is given a dataset consisting of $n$ samples $\mathbf{T}_{1:n}$ of i.i.d. Gaussian tensors of order $k$ with the promise that $\mathbb{E}\mathbf{T}_1$ is a rank-1 tensor and $\|\mathbb{E} \mathbf{T}_1\| = 1$. The goal is to estimate $\mathbb{E} \mathbf{T}_1$. This problem exhibits a large conjectured hard phase when $k>2$: When $d \lesssim n \ll d^{\frac{k}{2}}$ it is information theoretically possible to estimate $\mathbb{E} \mathbf{T}_1$, but no polynomial time estimator is known. We provide a sharp analysis of the optimal sample complexity in the Statistical Query (SQ) model and show that SQ algorithms with polynomial query complexity not only fail to solve Tensor PCA in the conjectured hard phase, but also have a strictly sub-optimal sample complexity compared to some polynomial time estimators such as the Richard-Montanari spectral estimator. Our analysis reveals that the optimal sample complexity in the SQ model depends on whether $\mathbb{E} \mathbf{T}_1$ is symmetric or not. For symmetric, even order tensors, we also isolate a sample size regime in which it is possible to test if $\mathbb{E} \mathbf{T}_1 = \mathbf{0}$ or $\mathbb{E}\mathbf{T}_1 \neq \mathbf{0}$ with polynomially many queries but not estimate $\mathbb{E}\mathbf{T}_1$. Our proofs rely on the Fourier analytic approach of Feldman, Perkins and Vempala (2018) to prove sharp SQ lower bounds.

math.ST↗

arXiv2021

Consistent Risk Estimation in Moderately High-Dimensional Linear Regression

Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical properties of such estimates have been extensively studied in the low-dimensional settings, where the number of predictors $p$ is much smaller than the number of observations $n$. However, a unifying methodology accompanied with a rigorous theory is lacking in high-dimensional settings. This paper studies the problem of risk estimation under the moderately high-dimensional asymptotic setting $n,p \rightarrow \infty$ and $n/p \rightarrow δ>1$ ($δ$ is a fixed number), and proves the consistency of three risk estimates that have been successful in numerical studies, i.e., leave-one-out cross validation (LOOCV), approximate leave-one-out (ALO), and approximate message passing (AMP)-based techniques. A corner stone of our analysis is a bound that we obtain on the discrepancy of the `residuals' obtained from AMP and LOOCV. This connection not only enables us to obtain a more refined information on the estimates of AMP, ALO, and LOOCV, but also offers an upper bound on the convergence rate of each estimate.

math.ST↗

arXiv2020

Biased Programmers? Or Biased Data? A Field Experiment in Operationalizing AI Ethics

Why do biased predictions arise? What interventions can prevent them? We evaluate 8.2 million algorithmic predictions of math performance from $\approx$400 AI engineers, each of whom developed an algorithm under a randomly assigned experimental condition. Our treatment arms modified programmers' incentives, training data, awareness, and/or technical knowledge of AI ethics. We then assess out-of-sample predictions from their algorithms using randomized audit manipulations of algorithm inputs and ground-truth math performance for 20K subjects. We find that biased predictions are mostly caused by biased training data. However, one-third of the benefit of better training data comes through a novel economic mechanism: Engineers exert greater effort and are more responsive to incentives when given better training data. We also assess how performance varies with programmers' demographic characteristics, and their performance on a psychological test of implicit bias (IAT) concerning gender and careers. We find no evidence that female, minority and low-IAT engineers exhibit lower bias or discrimination in their code. However, we do find that prediction errors are correlated within demographic groups, which creates performance improvements through cross-demographic averaging. Finally, we quantify the benefits and tradeoffs of practical managerial or policy interventions such as technical advice, simple reminders, and improved incentives for decreasing algorithmic bias.

econ.GN↗

arXiv2020

Interpreting deep learning models for weak lensing

Deep Neural Networks (DNNs) are powerful algorithms that have been proven capable of extracting non-Gaussian information from weak lensing (WL) data sets. Understanding which features in the data determine the output of these nested, non-linear algorithms is an important but challenging task. We analyze a DNN that has been found in previous work to accurately recover cosmological parameters in simulated maps of the WL convergence ($κ$). We derive constraints on the cosmological parameter pair $(Ω_m,σ_8)$ from a combination of three commonly used WL statistics (power spectrum, lensing peaks, and Minkowski functionals), using ray-traced simulated $κ$ maps. We show that the network can improve the inferred parameter constraints relative to this combination by $20\%$ even in the presence of realistic levels of shape noise. We apply a series of well established saliency methods to interpret the DNN and find that the most relevant pixels are those with extreme $κ$ values. For noiseless maps, regions with negative $κ$ account for $86-69\%$ of the attribution of the DNN output, defined as the square of the saliency in input space. In the presence of shape nose, the attribution concentrates in high convergence regions, with $36-68\%$ of the attribution in regions with $κ> 3 σ_κ$.

astro-ph.CO↗

arXiv2020

Ensuring Fairness Beyond the Training Data

We initiate the study of fair classifiers that are robust to perturbations in the training distribution. Despite recent progress, the literature on fairness has largely ignored the design of fair and robust classifiers. In this work, we develop classifiers that are fair not only with respect to the training distribution, but also for a class of distributions that are weighted perturbations of the training samples. We formulate a min-max objective function whose goal is to minimize a distributionally robust training loss, and at the same time, find a classifier that is fair with respect to a class of distributions. We first reduce this problem to finding a fair classifier that is robust with respect to the class of distributions. Based on online learning algorithm, we develop an iterative algorithm that provably converges to such a fair and robust solution. Experiments on standard machine learning fairness datasets suggest that, compared to the state-of-the-art fair classifiers, our classifier retains fairness guarantees and test accuracy for a large class of perturbations on the test set. Furthermore, our experiments show that there is an inherent trade-off between fairness robustness and accuracy of such classifiers.

cs.LG↗

arXiv2020

Detecting Foodborne Illness Complaints in Multiple Languages Using English Annotations Only

Health departments have been deploying text classification systems for the early detection of foodborne illness complaints in social media documents such as Yelp restaurant reviews. Current systems have been successfully applied for documents in English and, as a result, a promising direction is to increase coverage and recall by considering documents in additional languages, such as Spanish or Chinese. Training previous systems for more languages, however, would be expensive, as it would require the manual annotation of many documents for each new target language. To address this challenge, we consider cross-lingual learning and train multilingual classifiers using only the annotations for English-language reviews. Recent zero-shot approaches based on pre-trained multi-lingual BERT (mBERT) have been shown to effectively align languages for aspects such as sentiment. Interestingly, we show that those approaches are less effective for capturing the nuances of foodborne illness, our public health application of interest. To improve performance without extra annotations, we create artificial training documents in the target language through machine translation and train mBERT jointly for the source (English) and target language. Furthermore, we show that translating labeled documents to multiple languages leads to additional performance improvements for some target languages. We demonstrate the benefits of our approach through extensive experiments with Yelp restaurant reviews in seven languages. Our classifiers identify foodborne illness complaints in multilingual reviews from the Yelp Challenge dataset, which highlights the potential of our general approach for deployment in health departments.

cs.CL↗

arXiv2020

Two models of double descent for weak features

The "double descent" risk curve was proposed to qualitatively describe the out-of-sample prediction accuracy of variably-parameterized machine learning models. This article provides a precise mathematical analysis for the shape of this curve in two simple data models with the least squares/least norm predictor. Specifically, it is shown that the risk peaks when the number of features $p$ is close to the sample size $n$, but also that the risk decreases towards its minimum as $p$ increases beyond $n$. This behavior is contrasted with that of "prescient" models that select features in an a priori optimal order.

cs.LG↗

arXiv2020

Cross-Lingual Text Classification with Minimal Resources by Transferring a Sparse Teacher

Cross-lingual text classification alleviates the need for manually labeled documents in a target language by leveraging labeled documents from other languages. Existing approaches for transferring supervision across languages require expensive cross-lingual resources, such as parallel corpora, while less expensive cross-lingual representation learning approaches train classifiers without target labeled documents. In this work, we propose a cross-lingual teacher-student method, CLTS, that generates "weak" supervision in the target language using minimal cross-lingual resources, in the form of a small number of word translations. Given a limited translation budget, CLTS extracts and transfers only the most important task-specific seed words across languages and initializes a teacher classifier based on the translated seed words. Then, CLTS iteratively trains a more powerful student that also exploits the context of the seed words in unlabeled target documents and outperforms the teacher. CLTS is simple and surprisingly effective in 18 diverse languages: by transferring just 20 seed words, even a bag-of-words logistic regression student outperforms state-of-the-art cross-lingual methods (e.g., based on multilingual BERT). Moreover, CLTS can accommodate any type of student classifier: leveraging a monolingual BERT student leads to further improvements and outperforms even more expensive approaches by up to 12% in accuracy. Finally, CLTS addresses emerging tasks in low-resource languages using just a small number of word translations.

cs.CL↗