相关论文: Problem reduction, renormalization, and memory
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…
Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…
Recurrent neural networks have proved to be an effective method for statistical language modeling. However, in practice their memory and run-time complexity are usually too large to be implemented in real-time offline mobile applications.…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
We propose a new family of fairness definitions for classification problems that combine some of the best properties of both statistical and individual notions of fairness. We posit not only a distribution over individuals, but also a…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
Recurrent Neural Networks (RNNs) are widely used for modelling neural activity, yet the mathematical interplay of core procedures is used to analyze them (temporal rescaling, discretization, and linearization) remain uncharacterized. This…
Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently co-exist for the first time and are here reviewed, ranging from dominant ones such as statistical lossless compression…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power…