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Found 64 papers, 4 papers with code
An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization
In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls.
A general theory for robust clustering via trimmed mean
In this paper, we introduce a hybrid clustering technique with a novel multivariate trimmed mean type centroid estimate to produce mislabeling guarantees under a weak initialization condition for general error distributions around the centroids.
Structured Matrix Learning under Arbitrary Entrywise Dependence and Estimation of Markov Transition Kernel
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions.
Maximum Likelihood Estimation is All You Need for Well-Specified Covariate Shift
This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting.
Provably Efficient High-Dimensional Bandit Learning with Batched Feedbacks
For these settings, we design a provably sample-efficient algorithm which achieves a $ \mathcal{\tilde O}(s_0^2 \log^2 T)$ regret in the sparse case and $ \mathcal{\tilde O} ( r ^2 \log^2 T)$ regret in the low-rank case, using only $L = \mathcal{O}( \log T)$ batches.
Robust Transfer Learning with Unreliable Source Data
This paper addresses challenges in robust transfer learning stemming from ambiguity in Bayes classifiers and weak transferable signals between the target and source distribution.
Inferences on Mixing Probabilities and Ranking in Mixed-Membership Models
Network data is prevalent in numerous big data applications including economics and health networks where it is of prime importance to understand the latent structure of network.
Spectral Ranking Inferences based on General Multiway Comparisons
This paper studies the performance of the spectral method in the estimation and uncertainty quantification of the unobserved preference scores of compared entities in a general and more realistic setup.
UTOPIA: Universally Trainable Optimal Prediction Intervals Aggregation
Uncertainty quantification for prediction is an intriguing problem with significant applications in various fields, such as biomedical science, economic studies, and weather forecasts.
The Isotonic Mechanism for Exponential Family Estimation
We demonstrate that an author is incentivized to provide accurate rankings when her utility takes the form of a convex additive function of the adjusted review scores.
Minimax-Optimal Reward-Agnostic Exploration in Reinforcement Learning
This paper studies reward-agnostic exploration in reinforcement learning (RL) -- a scenario where the learner is unware of the reward functions during the exploration stage -- and designs an algorithm that improves over the state of the art.
Environment Invariant Linear Least Squares
To the best of our knowledge, this paper is the first to realize statistically efficient invariance learning in the general linear model.
On the Provable Advantage of Unsupervised Pretraining
Unsupervised pretraining, which learns a useful representation using a large amount of unlabeled data to facilitate the learning of downstream tasks, is a critical component of modern large-scale machine learning systems.
Communication-Efficient Distributed Estimation and Inference for Cox's Model
Motivated by multi-center biomedical studies that cannot share individual data due to privacy and ownership concerns, we develop communication-efficient iterative distributed algorithms for estimation and inference in the high-dimensional sparse Cox proportional hazards model.
Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension
We show that under certain standard assumptions, debiased deep neural networks achieve a minimax optimal rate both in terms of $(n, d)$.
Uncertainty Quantification of MLE for Entity Ranking with Covariates
This paper concerns with statistical estimation and inference for the ranking problems based on pairwise comparisons with additional covariate information such as the attributes of the compared items.
Robust High-dimensional Tuning Free Multiple Testing
A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference.
Ranking Inferences Based on the Top Choice of Multiway Comparisons
The estimated distribution is then used to construct simultaneous confidence intervals for the differences in the preference scores and the ranks of individual items.
SIMPLE-RC: Group Network Inference with Non-Sharp Nulls and Weak Signals
To address these practical challenges, in this paper we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the non-sharp null hypothesis that a group of given nodes share similar (not necessarily identical) membership profiles under weaker signals.
Factor-Augmented Regularized Model for Hazard Regression
A prevalent feature of high-dimensional data is the dependence among covariates, and model selection is known to be challenging when covariates are highly correlated.
Strategic Decision-Making in the Presence of Information Asymmetry: Provably Efficient RL with Algorithmic Instruments
We study offline reinforcement learning under a novel model called strategic MDP, which characterizes the strategic interactions between a principal and a sequence of myopic agents with private types.
Robust Matrix Completion with Heavy-tailed Noise
This paper studies low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries.
Model-Based Reinforcement Learning for Offline Zero-Sum Markov Games
This paper makes progress towards learning Nash equilibria in two-player zero-sum Markov games from offline data.
Model-based Reinforcement Learning
reinforcement-learning
+1
How do noise tails impact on deep ReLU networks?
This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment.
The Efficacy of Pessimism in Asynchronous Q-Learning
This paper is concerned with the asynchronous form of Q-learning, which applies a stochastic approximation scheme to Markovian data samples.
Are Latent Factor Regression and Sparse Regression Adequate?
To fill in such an important gap, we also leverage our model as the alternative model to test the sufficiency of the latent factor regression and the sparse linear regression models.
Curriculum Learning for Vision-and-Language Navigation
Vision-and-Language Navigation (VLN) is a task where an agent navigates in an embodied indoor environment under human instructions.
Policy Optimization Using Semi-parametric Models for Dynamic Pricing
$F(\cdot)$ with $m$-th order derivative ($m\geq 2$), our policy achieves a regret upper bound of $\tilde{O}_{d}(T^{\frac{2m+1}{4m-1}})$, where $T$ is time horizon and $\tilde{O}_{d}$ is the order that hides logarithmic terms and the dimensionality of feature $d$.
Constructing Phrase-level Semantic Labels to Form Multi-Grained Supervision for Image-Text Retrieval
Existing research for image text retrieval mainly relies on sentence-level supervision to distinguish matched and mismatched sentences for a query image.
Inference for Heteroskedastic PCA with Missing Data
This paper studies how to construct confidence regions for principal component analysis (PCA) in high dimension, a problem that has been vastly under-explored.
Sample-Efficient Reinforcement Learning for Linearly-Parameterized MDPs with a Generative Model
Our results show that for arbitrarily large-scale MDP, both the model-based approach and Q-learning are sample-efficient when $K$ is relatively small, and hence the title of this paper.
Bridging factor and sparse models
Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions.
The Interplay of Demographic Variables and Social Distancing Scores in Deep Prediction of U.S. COVID-19 Cases
With the severity of the COVID-19 outbreak, we characterize the nature of the growth trajectories of counties in the United States using a novel combination of spectral clustering and the correlation matrix.
Spectral Methods for Data Science: A Statistical Perspective
While the studies of spectral methods can be traced back to classical matrix perturbation theory and methods of moments, the past decade has witnessed tremendous theoretical advances in demystifying their efficacy through the lens of statistical modeling, with the aid of non-asymptotic random matrix theory.
Do We Exploit all Information for Counterfactual Analysis? Benefits of Factor Models and Idiosyncratic Correction
The data consist of daily sales and prices of five different products over more than 400 municipalities.
Recent Developments on Factor Models and its Applications in Econometric Learning
This paper makes a selective survey on the recent development of the factor model and its application on statistical learnings.
Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution under Random Designs
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i. e.$~$a sort of random Fourier design and Gaussian design).
Understanding Implicit Regularization in Over-Parameterized Single Index Model
For both the vector and matrix settings, we construct an over-parameterized least-squares loss function by employing the score function transform and a robust truncation step designed specifically for heavy-tailed data.
An $\ell_p$ theory of PCA and spectral clustering
Principal Component Analysis (PCA) is a powerful tool in statistics and machine learning.
Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data
This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data.
SIMPLE: Statistical Inference on Membership Profiles in Large Networks
Both tests are of the Hotelling-type statistics based on the rows of empirical eigenvectors or their ratios, whose asymptotic covariance matrices are very challenging to derive and estimate.
Communication-Efficient Accurate Statistical Estimation
In addition, we give the conditions under which the one-step CEASE estimator is statistically efficient.
Inference and Uncertainty Quantification for Noisy Matrix Completion
As a byproduct, we obtain a sharp characterization of the estimation accuracy of our de-biased estimators, which, to the best of our knowledge, are the first tractable algorithms that provably achieve full statistical efficiency (including the preconstant).
Low-Rank Principal Eigenmatrix Analysis
Sparse PCA is a widely used technique for high-dimensional data analysis.
A Selective Overview of Deep Learning
Deep learning has arguably achieved tremendous success in recent years.
Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization
This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently.
A Theoretical Analysis of Deep Q-Learning
Despite the great empirical success of deep reinforcement learning, its theoretical foundation is less well understood.
Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices
The aim is to estimate the leading eigenvalue and eigenvector of $\mathbf{M}^{\star}$.
Curse of Heterogeneity: Computational Barriers in Sparse Mixture Models and Phase Retrieval
We study the fundamental tradeoffs between statistical accuracy and computational tractability in the analysis of high dimensional heterogeneous data.
Robust high dimensional factor models with applications to statistical machine learning
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance.
Tensor Methods for Additive Index Models under Discordance and Heterogeneity
Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models.
Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples $y_{i}=(\mathbf{a}_{i}^{\top}\mathbf{x}^{\natural})^{2}$, $1\leq i\leq m$.
Testability of high-dimensional linear models with non-sparse structures
Uniform non-testability identifies a collection of alternatives such that the power of any test, against any alternative in the group, is asymptotically at most equal to the nominal size.
Spectral Method and Regularized MLE Are Both Optimal for Top-$K$ Ranking
This paper is concerned with the problem of top-$K$ ranking from pairwise comparisons.
Adaptive Huber Regression
We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when $\delta \geq 1$, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime $0<\delta< 1$.
Statistics Theory Methodology Statistics Theory
Factor-Adjusted Regularized Model Selection
This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency.
Methodology
Sufficient Forecasting Using Factor Models
Our method and theory allow the number of predictors to be larger than the number of observations.
A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models
Measuring conditional dependence is an important topic in statistics with broad applications including graphical models.
High Dimensional Semiparametric Latent Graphical Model for Mixed Data
Theoretically, the proposed methods achieve the same rates of convergence for both precision matrix estimation and eigenvector estimation, as if the latent variables were observed.
Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification
We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities.
Challenges of Big Data Analysis
Big Data bring new opportunities to modern society and challenges to data scientists.
Strong oracle optimality of folded concave penalized estimation
Folded concave penalization methods have been shown to enjoy the strong oracle property for high-dimensional sparse estimation.
Regularization for Cox's proportional hazards model with NP-dimensionality
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection.
