arXiv research

An algorithm finds the maximum entry of a stochastic low-rank matrix from noisy observations.

PACE-GGM uses Gaussian mechanism for private covariance estimation.

In a broad range of classification and decision making problems, one is given the advice or predictions of several classifiers, of unknown reliability, over multiple questions or queries. This scenario is different from the standard supervised setting, where each classifier accuracy can be assessed using available labe…

Estimates missing distributions using nearest neighbors with kernel methods.

Study exact community detection in k-community Gaussian mixtures with different intensities.

New tensor completion method reduces impact of outliers.

A novel regularizer of the PARAFAC decomposition factors capturing the tensor's rank is proposed in this paper, as the key enabler for completion of three-way data arrays with missing entries. Set in a Bayesian framework, the tensor completion method incorporates prior information to enhance its smoothing and predictio…

Motivated by the industry practice of pairs trading, we study the optimal timing strategies for trading a mean-reverting price spread. An optimal double stopping problem is formulated to analyze the timing to start and subsequently liquidate the position subject to transaction costs. Modeling the price spread by an Orn…

We consider the problem of low canonical polyadic (CP) rank tensor completion. A completion is a tensor whose entries agree with the observed entries and its rank matches the given CP rank. We analyze the manifold structure corresponding to the tensors with the given rank and define a set of polynomials based on the sa…

Algorithm estimates tensors from sparse observations with robust error bounds.

New MIMO constellation design for noncoherent communications reduces hardware complexity.

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix $M$, and establish theoretical upper and lower bounds on the rec…

Convex optimization method infers latent structure in random dot product graphs.

Spectral ranking methods are improved against semi-random graph sampling.

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of noisy 1-bit (or binary) measurements generated according to a probabilistic model. W…

We solve a challenging factor analysis problem using ML principle and scalable algorithms.

The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of its entries. Here, we investigate the case of highly quantized observations when …

AI models failed to profitably predict cryptocurrency extrema on Binance Spot.

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) and the adaptive LASSO penalty (Zou, 2006) hav…

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.

Proposes a deep model for geometric matrix completion.

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

Consider a noisy linear observation model with an unknown permutation, based on observing $y = Π^* A x^* + w$, where $x^* \in \mathbb{R}^d$ is an unknown vector, $Π^*$ is an unknown $n \times n$ permutation matrix, and $w \in \mathbb{R}^n$ is additive Gaussian noise. We analyze the problem of permutation recovery in a …

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

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with pro…

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well known techniques in da…

We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces. The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed e…

Study of asymmetric rank-one tensor models with non-Gaussian noise.

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…

Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn the structure of the graph by estimating a sparse inverse covariance matrix from…

Modern applications and progress in deep learning research have created renewed interest for generative models of text and of images. However, even today it is unclear what objective functions one should use to train and evaluate these models. In this paper we present two contributions. Firstly, we present a critique o…

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.

Develops a method to complete binary matrices using all types of observed entries.

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

Study shows how leveraging hierarchical similarity graphs improves matrix completion in recommender systems.

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…

SGMM clusters data in one pass, reducing dimensionality.

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…