Related papers: The Causal Complementation Algorithm for Lifting F…

Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional…

Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…

We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix $A$, such a factorization provides a low rank approximate decomposition of the form $A \approx C U R$, where $C$ and $R$…

Defining the number of latent factors has been one of the most challenging problems in factor analysis. Infinite factor models offer a solution to this problem by applying increasing shrinkage on the columns of factor loading matrices, thus…

Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…

Uplift modeling is crucial in various applications ranging from marketing and policy-making to personalized recommendations. The main objective is to learn optimal treatment allocations for a heterogeneous population. A primary line of…

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update…

In this work, we highlight a connection between the incremental proximal method and stochastic filters. We begin by showing that the proximal operators coincide, and hence can be realized with, Bayes updates. We give the explicit form of…

The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for non-symmetric saddle point linear algebraic systems. The strategy is applied to solve…

Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…

Causal analysis has become an essential component in understanding the underlying causes of phenomena across various fields. Despite its significance, existing literature on causal discovery algorithms is fragmented, with inconsistent…

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…

Causal discovery and causal effect estimation are two fundamental tasks in causal inference. While many methods have been developed for each task individually, statistical challenges arise when applying these methods jointly: estimating…

Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…

A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure…

A new hybrid algorithm for LDU-factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver…

We show that given a nonvanishing particular solution of the equation (divpgrad+q)u=0 (1) the corresponding differential operator can be factorized into a product of two first order operators. The factorization allows us to reduce the…

Hybrid Bayesian networks (HBN) contain complex conditional probabilistic distributions (CPD) specified as partitioned expressions over discrete and continuous variables. The size of these CPDs grows exponentially with the number of parent…