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Found 19 papers, 1 papers with code
Guaranteed Rank Minimization via Singular Value Projection
Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics.
Matrix Completion from Power-Law Distributed Samples
In this paper, we propose a graph theoretic approach to matrix completion that solves the problem for more realistic sampling models.
Computational Limits for Matrix Completion
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries.
Learning Graphical Models Using Multiplicative Weights
Our main application is an algorithm for learning the structure of t-wise MRFs with nearly-optimal sample complexity (up to polynomial losses in necessary terms that depend on the weights) and running time that is $n^{O(t)}$.
Learning One Convolutional Layer with Overlapping Patches
We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches.
Efficient Algorithms for Outlier-Robust Regression
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels.
Learning Some Popular Gaussian Graphical Models without Condition Number Bounds
While there are a variety of algorithms (e. g. Graphical Lasso, CLIME) that provably recover the graph structure with a logarithmic number of samples, they assume various conditions that require the precision matrix to be in some sense well-conditioned.
Learning Polynomials of Few Relevant Dimensions
We give an algorithm that learns the polynomial within accuracy $\epsilon$ with sample complexity that is roughly $N = O_{r, d}(n \log^2(1/\epsilon) (\log n)^d)$ and runtime $O_{r, d}(N n^2)$.
Learning Deep ReLU Networks Is Fixed-Parameter Tractable
These results provably cannot be obtained using gradient-based methods and give the first example of a class of efficiently learnable neural networks that gradient descent will fail to learn.
On the Power of Preconditioning in Sparse Linear Regression
First, we show that the preconditioned Lasso can solve a large class of sparse linear regression problems nearly optimally: it succeeds whenever the dependency structure of the covariates, in the sense of the Markov property, has low treewidth -- even if $\Sigma$ is highly ill-conditioned.
Efficiently Learning Any One Hidden Layer ReLU Network From Queries
In this work we give the first polynomial-time algorithm for learning arbitrary one hidden layer neural networks activations provided black-box access to the network.
Efficiently Learning One Hidden Layer ReLU Networks From Queries
While the problem of PAC learning neural networks from samples has received considerable attention in recent years, in certain settings like model extraction attacks, it is reasonable to imagine having more than just the ability to observe random labeled examples.
Minimax Optimality (Probably) Doesn't Imply Distribution Learning for GANs
Arguably the most fundamental question in the theory of generative adversarial networks (GANs) is to understand to what extent GANs can actually learn the underlying distribution.
Hardness of Noise-Free Learning for Two-Hidden-Layer Neural Networks
We give superpolynomial statistical query (SQ) lower bounds for learning two-hidden-layer ReLU networks with respect to Gaussian inputs in the standard (noise-free) model.
Distributional Hardness Against Preconditioned Lasso via Erasure-Robust Designs
Surprisingly, at the heart of our lower bound is a new positive result in compressed sensing.
Learning Narrow One-Hidden-Layer ReLU Networks
We consider the well-studied problem of learning a linear combination of $k$ ReLU activations with respect to a Gaussian distribution on inputs in $d$ dimensions.
On User-Level Private Convex Optimization
We introduce a new mechanism for stochastic convex optimization (SCO) with user-level differential privacy guarantees.
Simple Mechanisms for Representing, Indexing and Manipulating Concepts
Deep networks typically learn concepts via classifiers, which involves setting up a model and training it via gradient descent to fit the concept-labeled data.
Lasso with Latents: Efficient Estimation, Covariate Rescaling, and Computational-Statistical Gaps
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations.
