arXiv research

Improved spectral method recovers sparse vectors in random subspaces.

Unified framework for structure learning via conditional independence testing.

Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing methods for ICA rely on and exploit strongly the assumption that S is not Gaussian…

Efficient bandit exploration for various distributions without distribution-specific tuning.

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identic…

Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations. Spike-and-slab (a.k.a. Bernoulli-Gaussian) priors are the gold standard f…

Study of a generalized geometric Brownian motion with varying entry and exit rates.

New research shows larger language models improve data processing for diverse entries.

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless…

For any matrix A in R^(m x n) of rank ρ, we present a probability distribution over the entries of A (the element-wise leverage scores of equation (2)) that reveals the most influential entries in the matrix. From a theoretical perspective, we prove that sampling at most s = O ((m + n) ρ^2 ln (m + n)) entries of the ma…

Improved matrix completion for non-uniformly sampled data.

Study on optimal bubble riding with price-dependent entry times in a mean field game model.

Research shows how deepfakes can be used to manipulate accounting systems.

We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More s…

Paper improves tensor completion by reducing sample entries needed.

Reducing barriers to entry in large-scale ML markets, study shows multi-objective learning can lower data requirements.

A new tensor completion method handles missing data with missing not at random entries.

Groups of matrices with integer-like entries are studied.

Study on market entry timing in stock liquidation with trading constraints.

The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random entries, and performance in achieving small reconstruction error. We propose a …

Estimates low-rank distributional matrices from incomplete samples.

Scalable and robust TR decomposition for large-scale data with missing entries and outliers.

In this paper, we consider the streaming memory-limited matrix completion problem when the observed entries are noisy versions of a small random fraction of the original entries. We are interested in scenarios where the matrix size is very large so the matrix is very hard to store and manipulate. Here, columns of the o…

We give an algorithm for completing an order-$m$ symmetric low-rank tensor from its multilinear entries in time roughly proportional to the number of tensor entries. We apply our tensor completion algorithm to the problem of learning mixtures of product distributions over the hypercube, obtaining new algorithmic result…

The covariance matrix of a $p$-dimensional random variable is a fundamental quantity in data analysis. Given $n$ i.i.d. observations, it is typically estimated by the sample covariance matrix, at a computational cost of $O(np^{2})$ operations. When $n,p$ are large, this computation may be prohibitively slow. Moreover, …

A matrix completion problem, which aims to recover a complete matrix from its partial observations, is one of the important problems in the machine learning field and has been studied actively. However, there is a discrepancy between the mainstream problem setting, which assumes continuous-valued observations, and some…

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a…

A new method for streaming PCA provides confidence intervals for eigenvector entries.

PACE-GGM uses Gaussian mechanism for private covariance estimation.

Current generation of memory-augmented neural networks has limited scalability as they cannot efficiently process data that are too large to fit in the external memory storage. One example of this is lifelong learning scenario where the model receives unlimited length of data stream as an input which contains vast majo…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …

Let M be a random (alpha n) x n matrix of rank r<<n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(rn) observed entries with relative root mean square error RMSE <= C(rn/|E|)^0.5 . Further, if r=O(1), M can be reconstructed ex…

New spectral methods improve matrix estimation in RL with low-rank structure.

TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.

A new method detects and compacts saturated entries in antisparse coding.

In this paper, we consider matrix completion from non-uniformly sampled entries including fully observed and partially observed columns. Specifically, we assume that a small number of columns are randomly selected and fully observed, and each remaining column is partially observed with uniform sampling. To recover the …

We study algebraic properties of matrices whose rows are mutual neighbours, and are also neigbours of 0 ("neighbour" in the sense of a certain nilpotency condition). The intended application is in synthetic differential geometry. For a square matrix of this kind, the product of the diagonal entries equals the determina…

Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an imbalanced learning problem, since the scale of missing entries is usually much…

The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each missing entry, and then train a prediction model with the new dataset. A drawbac…

Researchers have proposed hardware, software, and algorithmic optimizations to improve the computational performance of deep learning. While some of these optimizations perform the same operations faster (e.g., increasing GPU clock speed), many others modify the semantics of the training procedure (e.g., reduced precis…

New algorithm optimizes positions of CountSketch non-zero entries for better data compression.

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the underlying matrix has rank $r=1$, has positive bounded entries, and the graph $\mathcal{G…

Study heavy-tailed weights' impact on neural network's spectral distribution.

We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tr…

Method uses optimal transport to complete distributional matrices.

The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a clustering algorithm, that will provide good clustering even in the presence of missin…

New matrix completion method for arbitrary sampling patterns using network flows.

Proposes a nonparametric tensor factorization for sparse data.