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Feb 23, 2017
Machine Learning

In this paper we show if a generative model can be expressed as the composition of n Barron functions, then it can be approximated by a n+1-layer neural network. Along the way we proved a multi-layer version of the Barron’s Theorem [Barron1993], and…

On the ability of neural nets to express distributions

Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution---also theoretically not understood---concerns t…
Apr 09, 2012
Machine Learning
Data Structures and Algorithms
Information Retrieval

Learning Topic Models - Going beyond SVD

Topic Modeling is an approach used for automatic comprehension and classification of data in a variety of settings, and perhaps the canonical applica…
Jun 14, 2019
Machine Learning

Explaining Landscape Connectivity of Low-cost Solutions for Multilaye…

Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima---at least those discovered by gradient-based optimization---…
May 20, 2019
Machine Learning
Discrete Mathematics
Social and Information Networks

Random Walks on Hypergraphs with Edge-Dependent Vertex Weights

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectra…
Jun 29, 2019
Computer Vision
Machine Learning

Learning to Generate Synthetic 3D Training Data through Hybrid Gradie…

Synthetic images rendered by graphics engines are a promising source for training deep networks. However, it is challenging to ensure that they can h…
Nov 01, 2016
Data Structures and Algorithms

Submodular Maximization over Sliding Windows

In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the …
Aug 25, 2014
Machine Learning

Improved Distributed Principal Component Analysis

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the un…
Aug 10, 2011
Computer Science and Game Theory

On the Structure of Weakly Acyclic Games

The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a wea…
Feb 06, 2016
Conferences: ICML
Machine Learning
Data Structures and Algorithms

Recovery guarantee of weighted low-rank approximation via alternating…

Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated…
May 14, 2019
Signal Processing
Data Structures and Algorithms
Machine Learning
Statistics Theory

Sample Efficient Toeplitz Covariance Estimation

We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assump…
May 24, 2019
Machine Learning

Sequential Gaussian Processes for Online Learning of Nonstationary …

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated …
Dec 19, 2012
Machine Learning
Data Structures and Algorithms

A Practical Algorithm for Topic Modeling with Provable Guarantees

Topic models provide a useful method for dimensionality reduction and exploratory data analysis in large text corpora. Most approaches to topic model…
Jun 07, 2014
Conferences: NIPS
Machine Learning

A Drifting-Games Analysis for Online Learning and Applications to B…

We provide a general mechanism to design online learning algorithms based on a minimax analysis within a drifting-games framework. Different online l…
Dec 08, 2016
Computer Vision

Joint Hand Detection and Rotation Estimation by Using CNN

Hand detection is essential for many hand related tasks, e.g. parsing hand pose, understanding gesture, which are extremely useful for robotics and h…
Nov 12, 2007
Data Structures and Algorithms

Data Structures for Mergeable Trees

Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. Th…
Jun 13, 2018
Machine Learning

On Tighter Generalization Bound for Deep Neural Networks: CNNs, ResNe…

We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, a…
Nov 30, 2009
Computational Complexity
Data Structures and Algorithms

Subsampling Mathematical Relaxations and Average-case Complexity

We initiate a study of when the value of mathematical relaxations such as linear and semidefinite programs for constraint satisfaction problems (CSPs…
May 28, 2019
Machine Learning
Artificial Intelligence

A Simple Saliency Method That Passes the Sanity Checks

There is great interest in *saliency methods* (also called *attribution methods*), which give "explanations" for a deep net's decision, by assigning …
May 28, 2019
Machine Learning
Artificial Intelligence

A Simple Saliency Method That Passes the Sanity Checks

There is great interest in "saliency methods" (also called "attribution methods"), which give "explanations" for a deep net's decision, by assigning …
Apr 15, 2018
Computer Vision

Semantic Feature Augmentation in Few-shot Learning

A fundamental problem with few-shot learning is the scarcity of data in training. A natural solution to alleviate this scarcity is to augment the exi…
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