Related papers: An Approximation of the First Order Marcum $Q$-Fun…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
The modified Bessel function of the first kind, $I_{\nu}(x)$, arises in numerous areas of study, such as physics, signal processing, probability, statistics, etc. As such, there has been much interest in recent years in deducing properties…
We study online estimation in latent-variable models by recasting the problem as tracking a moving empirical equilibrium. Standard online EM and stochastic approximation analyses primarily study convergence toward the population parameter…
Recent advances in Model Predictive Control (MPC) leveraging a combination of first-order methods, such as the Alternating Direction Method of Multipliers (ADMM), and offline precomputation and caching of select operations, have excitingly…
We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes…
We consider the problem of optimally compressing and caching data across a communication network. Given the data generated at edge nodes and a routing path, our goal is to determine the optimal data compression ratios and caching decisions…
As we all known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing and signal processing etc. In this paper, an algorithm for nonnegative matrix…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability…
The aim of this work is the derivation of two approximated expressions for the two dimensional Gaussian Q-function, $Q(x,y;\rho)$. These expressions are highly accurate and are expressed in closed-form. Furthermore, their algebraic…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
We aim to create the highest possible quality of treatment-control matches for categorical data in the potential outcomes framework. Matching methods are heavily used in the social sciences due to their interpretability, but most matching…
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral…
We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and…
In this paper we give an explicit solution to the rank constrained matrix approximation in Frobenius norm, which is a generalization of the classical approximation of an m by n matrix A by a matrix of rank k at most.
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…