arXiv research

Characterizes connections on normal distributions manifold.

Study on lightlike submanifolds in statistical manifold geometry.

New statistics are introduced that maintain the Fisher metric structure closely, akin to sufficient statistics.

Characterizes connections on multivariate normal distributions.

New formulae identify discrete probability laws without needing normalization constants.

This paper characterizes projective models in statistical relational learning.

Statistical query (SQ) algorithms are algorithms that have access to an {\em SQ oracle} for the input distribution $D$ instead of i.i.d.~ samples from $D$. Given a query function $φ:X \rightarrow [-1,1]$, the oracle returns an estimate of ${\bf E}_{ x\sim D}[φ(x)]$ within some tolerance $τ_φ$ that roughly corresponds t…

This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves. We a…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix estimation, and noisy matrix completion. We propose computationally feasible conv…

The paper explores quantum statistical manifolds and their autoparallelity, providing estimation-theoretical characterizations.

Normalizing flows improve ptychography reconstruction quality and uncertainty quantification.

Deep learning architectures have demonstrated state-of-the-art performance for object classification and have become ubiquitous in commercial products. These methods are often applied without understanding (a) the difficulty of a classification task given the input data, and (b) how a specific deep learning architectur…

We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal beha…

The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.

Discovering statistically significant patterns from databases is an important challenging problem. The main obstacle of this problem is in the difficulty of taking into account the selection bias, i.e., the bias arising from the fact that patterns are selected from extremely large number of candidates in databases. In …

Study CR-statistical submanifolds in holomorphic statistical spaces.

Unified framework for disentangled representations using mechanistic independence.

Sharp inequalities and solitons studied in statistical submersions.

This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…

Unified method for MMD variance estimation improves accuracy and computational efficiency.

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been used for this task which enjoy fewer assumptions on the distributions than the parametric approach and can handle high-dimensional data. In this paper we focus on th…

Paper characterizes gradient descent in high-dimensional learning problems.

The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.

We present cross and time series analysis of price fluctuations in the U.S. Treasury fixed income market. By means of techniques borrowed from statistical physics we show that the correlation among bonds depends strongly on the maturity and bonds' price increments do not fulfill the random walk hyphoteses.

Combinatorial dimensions play an important role in the theory of machine learning. For example, VC dimension characterizes PAC learning, SQ dimension characterizes weak learning with statistical queries, and Littlestone dimension characterizes online learning. In this paper we aim to develop combinatorial dimensions th…

We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by extracting its first four central moments. We observe that these moments are fl…

This paper reviews statistical and machine learning methods for anti-money laundering.

Recently we reported on an application of the Tsallis non-extensive statistics to the S&P500 stock index. There we argued that the statistics are applicable to a broad range of markets and exchanges where anamolous (super) diffusion and 'heavy' tails of the distribution are present, as they are in the S&P500. We have c…

Characterizes statistical complexity of realizable regression in PAC and online learning.

We propose a novel and flexible rank-breaking-then-composite-marginal-likelihood (RBCML) framework for learning random utility models (RUMs), which include the Plackett-Luce model. We characterize conditions for the objective function of RBCML to be strictly log-concave by proving that strict log-concavity is preserved…

Active inference framework improves $U$-statistic estimation efficiency.

Study characterizes bladder motion using dynamic MRI and statistical analysis.

Characterizes symmetric Bernoulli distributions with minimal convex sums.

Paper uses algebraic signatures to identify probabilistic structures in empirical data.

NN-Turb generates turbulent velocity statistics using neural networks.

We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…

New bandit algorithms focus on extreme values, outperforming existing methods.

Characterizes optimal reconstruction error in high-dimensional Gaussian mixtures.

New connections found on zero-mean multivariate normal distributions.

Generative models for graphs have been typically committed to strong prior assumptions concerning the form of the modeled distributions. Moreover, the vast majority of currently available models are either only suitable for characterizing some particular network properties (such as degree distribution or clustering coe…

New lattice path method for statistical inference of persistent diagrams.

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models…

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is we…

We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable criterion for risk measures, motivated by statistical considerations of forecasting. …

The complex, time-dependent statistical structures observed in the Dow Jones Industrial Average on a typical trading day are modeled with Lorentzian functions. The resonant-like structures are characterized by the values of the basic ratio: the average lifetime of the individual states associated with a given structura…

This work characterizes conditions for offline policy evaluation in reinforcement learning.

Characterizing the appearance of real-world surfaces is a fundamental problem in multidimensional reflectometry, computer vision and computer graphics. For many applications, appearance is sufficiently well characterized by the bidirectional reflectance distribution function (BRDF). We treat BRDF measurements as sample…

Multiple Sclerosis (MS) is a neurodegenerative disorder characterized by a complex set of clinical assessments. We use an unsupervised machine learning model called a Conditional Restricted Boltzmann Machine (CRBM) to learn the relationships between covariates commonly used to characterize subjects and their disease pr…