arXiv research

Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.

Algorithm estimates Gaussian parameters under unknown truncation sets.

Lower bound shows super-polynomial gap for estimating truncated Gaussian means.

The paper analyzes and mitigates biases in scalable Gaussian Process methods.

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal m…

The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…

Unified framework for mean testing under truncation bias.

Unified probabilistic framework for nonlinearities in neural networks.

EM algorithm converges to true mean for truncated mixtures of Gaussians.

New algorithms estimate parameters of Gaussian and non-Gaussian distributions from truncated samples.

The paper efficiently estimates parameters from truncated Gaussian and linear models.

New algorithm for truncated linear regression without knowing the survival set.

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel va…

New DP framework using data truncation for efficient estimation.

We show that $k$-means (Lloyd's algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian Mixture Models (GMM) with isotropic Gaussians. In contrast to the standard way to relate $k$-means and GMMs, the provided derivation shows that it is not required to consider Gau…

New method for constructing truncated vine copulas.

Truncated Lévy flights are random walks in which the arbitrarily large steps of a Lévy flight are eliminated. Since this makes the variance finite, the central limit theorem applies, and as time increases the probability distribution of the increments becomes Gaussian. Here, truncated Lévy flights with correlated fluct…

Efficiently estimates covariance for sub-Weibull vectors with sub-Gaussian rate.

Paper proposes using truncated normal distribution for RRC model, improving detection of minority classes.

We deal with the efficient parallelization of Bayesian global optimization algorithms, and more specifically of those based on the expected improvement criterion and its variants. A closed form formula relying on multivariate Gaussian cumulative distribution functions is established for a generalized version of the mul…

In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at …

New method optimizes weights and quantizers in ternary neural networks.

The paper models stock returns using $q$-Gaussians and negative binomials.

Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.

Optimized Franz-Parisi criterion matches SQ lower bounds for various statistical models.

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…

Improved robustness of gradient descent for low-rank matrix recovery in the presence of arbitrary outliers.

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and quadratic loss, SVM with Gaussian kernel can reach the almost optimal learning rate, p…

The paper presents a method to infer unknown forcing functions in differential equations using Gaussian processes and adjoints.

Proposes tGM-VAE for clustering and outlier detection in rs-fMRI.

We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents $α$ of the…

Exact selective inference with randomization for Gaussian regression models.

A novel approach termed \emph{stochastic truncated amplitude flow} (STAF) is developed to reconstruct an unknown $n$-dimensional real-/complex-valued signal $\bm{x}$ from $m$ `phaseless' quadratic equations of the form $ψ_i=|\langle\bm{a}_i,\bm{x}\rangle|$. This problem, also known as phase retrieval from magnitude-onl…

The paper estimates common mean of entangled Gaussians with bounded variances.

New bounds for optimal transport using Gaussian processes and rate-distortion functions.

New method for spatiotemporal data regression using Gaussian processes.

Study analyzes fluctuations in Mexican financial market index.

The paper tackles flexible modeling of constrained multimodal data.

The study assesses low-rank approximations in Gaussian Process regression.

The study assesses low-rank approximations in Gaussian Process regression.

Improved GP models for fast training and good performance.

Bayesian framework for sphere regression using Gaussian fields.

We propose a novel sparse tensor decomposition method, namely Tensor Truncated Power (TTP) method, that incorporates variable selection into the estimation of decomposition components. The sparsity is achieved via an efficient truncation step embedded in the tensor power iteration. Our method applies to a broad family …

Truncated CauchyNMF robustly learns subspaces from noisy data.

Efficiently estimate Boolean product distribution parameters from truncated samples.

In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, $W_t = B_t + μt, t\geq 0,$ where $(B_t)$ is a standard Brownian motion. Truncated variation differs from regular variation by neglect…