Related papers: statmod: Probability Calculations for the Inverse …
The Tsallis $q$-Gaussian distribution is a powerful generalization of the standard Gaussian distribution and is commonly used in various fields, including non-extensive statistical mechanics, financial markets and image processing. It…
I show how a renormalization group (RG) method can be used to incrementally integrate the information in cosmological large-scale structure data sets (including CMB, galaxy redshift surveys, etc.). I show numerical tests for Gaussian…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
The natural gradient method is widely used in statistical optimization, but its standard formulation assumes a Euclidean parameter space. This paper proposes an inversion-free stochastic natural gradient method for probability distributions…
Finite sample size corrections to the reparametrization-invariant solution of the inverse problem of probability are computed, and shown to converge uniformly to the correct distribution.
Summary: ipd is an open-source R software package for the downstream modeling of an outcome and its associated features where a potentially sizable portion of the outcome data has been imputed by an artificial intelligence or machine…
Covariate shift relaxes the widely-employed independent and identically distributed (IID) assumption by allowing different training and testing input distributions. Unfortunately, common methods for addressing covariate shift by trying to…
By formulating the inverse problem of partial differential equations (PDEs) as a statistical inference problem, the Bayesian approach provides a general framework for quantifying uncertainties. In the inverse problem of PDEs, parameters are…
Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The diffusion approximation of stochastic gradient descent (SGD) in current literature is only valid on a finite time interval. In this paper, we establish the uniform-in-time diffusion approximation of SGD, by only assuming that the…
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $\mathbb{P}(\sum_{i=1}^{N}{X_i} \leq \gamma)$, via importance sampling (IS). We…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
Generative models have shown strong potential as data-driven priors for solving inverse problems such as reconstructing medical images from undersampled measurements. While these priors improve reconstruction quality with fewer…