arXiv research

LITE efficiently estimates Gaussian PoM with linear time and memory complexity.

The paper integrates behavioral distortions into portfolio optimization using implied probability weighting functions.

Kernel embeddings separate distinct probability distributions, simplifying testing.

New findings on maximizing noise stability in partitions of Gaussian space.

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 between transformed variables. For finite discrete and jointly Gaussian random vari…

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is…

EMODM detects abnormal patterns in complex systems.

Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.

We consider a financial market model driven by an R^n-valued Gaussian process with stationary increments which is different from Brownian motion. This driving noise process consists of $n$ independent components, and each component has memory described by two parameters. For this market model, we explicitly solve optim…

Integrates VAEs into EM for deep clustering and generation.

We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced by traditional Markov Chain Monte Carlo (MCMC) samplers, through constructing pro…

DGMEs use Gaussian mixtures to quantify uncertainty in deep learning.

Building on the success of deep learning, two modern approaches to learn a probability model from the data are Generative Adversarial Networks (GANs) and Variational AutoEncoders (VAEs). VAEs consider an explicit probability model for the data and compute a generative distribution by maximizing a variational lower-boun…

New algorithm for fitting Gaussian mixtures using Wasserstein-Fisher-Rao geometry.

A new 1-iteration GMM learning algorithm improves robustness and accuracy.

In this paper, the problem of maximizing a black-box function $f:\mathcal{X} \to \mathbb{R}$ is studied in the Bayesian framework with a Gaussian Process (GP) prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query po…

A robust Gaussian process model using Huber likelihood for outlier resistance.

The paper proposes a new method for dictionary learning using $\ell_p$-norm maximization.

This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that function evaluations are costly. To select the next query point, we propose maximizing…

In order to cluster or partition data, we often use Expectation-and-Maximization (EM) or Variational approximation with a Gaussian Mixture Model (GMM), which is a parametric probability density function represented as a weighted sum of $\hat{K}$ Gaussian component densities. However, model selection to find underlying …

The paper analyzes generalization of noisy, iterative algorithms using maximal leakage.

Study utility maximization with delayed information in continuous time Gaussian markets.

Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones' Gaussian-process-based EGO algorithm. Instead of EGO's maximizing expected improvement, the MGSO use…

Geometric Gaussian approximations capture any distribution.

A new method for semi-supervised learning with missing data using GMM and margin confidence.

Bayesian approach approximates probability functions of Gaussian mixtures.

Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown…

Designs efficient algorithms to maximize the expectation of Gaussian random variables.

SQFA learns features maximizing Fisher-Rao distance for better classification.

NPMLE estimator automatically chooses the right model complexity for Gaussian mixtures.

The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely many bits. In this note, we characterise the quality of a code (i. e. a given en…

Paper uses GMM and MAF for probabilistic classification, outperforming simpler models.

In this paper, we develop a Bayesian evidence maximization framework to solve the sparse non-negative least squares (S-NNLS) problem. We introduce a family of probability densities referred to as the Rectified Gaussian Scale Mixture (R- GSM) to model the sparsity enforcing prior distribution for the solution. The R-GSM…

Information-Geometric Optimization (IGO) is a unified framework of stochastic algorithms for optimization problems. Given a family of probability distributions, IGO turns the original optimization problem into a new maximization problem on the parameter space of the probability distributions. IGO updates the parameter …

K-means fails in high dimensions with noise and few samples.

Two insurance companies collaborate to maximize the probability of none going bankrupt.

We extend Obata's rigidity theorem to free probability.

The paper examines utility maximization in markets with hidden Gaussian drift, finding restrictions on model parameters.

New method estimates Gaussian copulas with missing data using EM algorithm.

Generalized Chinese Remainder Theorem (CRT) has been shown to be a powerful approach to solve the ambiguity resolution problem. However, with its close relationship to number theory, study in this area is mainly from a coding theory perspective under deterministic conditions. Nevertheless, it can be proved that even wi…

In a regression setup with deterministic design, we study the pure aggregation problem and introduce a natural extension from the Gaussian distribution to distributions in the exponential family. While this extension bears strong connections with generalized linear models, it does not require identifiability of the par…

We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this regularization strategy yields low-complexity sparse models where the number of eff…

While Gaussian probability densities are omnipresent in applied mathematics, Gaussian cumulative probabilities are hard to calculate in any but the univariate case. We study the utility of Expectation Propagation (EP) as an approximate integration method for this problem. For rectangular integration regions, the approx…

PPM improves graph matching for correlated Gaussian Wigner models with high probability.

Optimizes target value in stochastic black box functions.

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …