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We introduce a probabilistic model with implicit norm regularization for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix…

Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is…

Schemes for exact multiplication of small matrices have a large symmetry group. This group defines an equivalence relation on the set of multiplication schemes. There are algorithms to decide whether two schemes are equivalent. However, for…

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…

Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a…

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Machine learning methods often assume that the test data have the same distribution as the training data. However, this assumption may not hold due to multiple levels of heterogeneity in applications, raising issues in algorithmic fairness…

Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…

We propose a vector linear programming formulation for a non-stationary, finite-horizon Markov decision process with vector-valued rewards. Pareto efficient policies are shown to correspond to efficient solutions of the linear program, and…

A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…

Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…

For a sufficiently nice 2 dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to a given pattern. For large approximating matrices, we observe that the…

Given a plane graph $G$ (i.e., a planar graph with a fixed planar embedding) and a simple cycle $C$ in $G$ whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar…

Many preference elicitation algorithms consider preference over propositional logic formulas or items with different attributes. In sequential decision making, a user's preference can be a preorder over possible outcomes, each of which is a…

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed…

Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…

We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…

A frame is an overcomplete set that can represent vectors(signals) faithfully and stably. Two frames are equivalent if signals can be essentially represented in the same way, which means two frames differ by a permutation, sign change or…