arXiv research

Paper offers a framework for estimating symmetric properties efficiently.

Paper proposes a method to design molecules with specific properties.

Concrete distribution properties examined on simplex.

Estimating properties of discrete distributions is a fundamental problem in statistical learning. We design the first unified, linear-time, competitive, property estimator that for a wide class of properties and for all underlying distributions uses just $2n$ samples to achieve the performance attained by the empirical…

The best-known and most commonly used distribution-property estimation technique uses a plug-in estimator, with empirical frequency replacing the underlying distribution. We present novel linear-time-computable estimators that significantly "amplify" the effective amount of data available. For a large variety of distri…

This note shows how independent elliptical distributions minimize the Wasserstein distance.

Study generalizes property elicitation to imprecise probabilities.

We study 'meta-dependence' in conditional independence tests across different empirical distributions.

Paper characterizes DLN distribution, its properties, and estimation methods.

Linear properties are either universal or absent across language models.

Investigates statistical properties of perturb-softmax and perturb-argmax distributions.

The study examines property testing and estimation under non-identically distributed samples, finding necessary and sufficient sample complexities.

Unified plug-in approach for estimating symmetric properties of distributions efficiently.

We argue that a stochastic model of economic exchange, whose steady-state distribution is a Generalized Beta Prime (also known as GB2), and some unique properties of the latter, are the reason for GB2's success in describing wealth/income distributions. We use housing sale prices as a proxy to wealth/income distributio…

Study properties of pointwise k-slant submanifolds in Kähler manifolds.

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal pro…

New research reveals how the pretraining distribution affects in-context learning in large language models.

Wide class of elliptically contoured distributions is a popular model of stock returns distribution. However the important question of adequacy of the model is open. There are some results which reject and approve such model. Such results are obtained by testing some properties of elliptical model for each pair of stoc…

This work investigates the properties of Gaussian-smoothed sliced divergences for comparing distributions.

We provide new results for noise-tolerant and sample-efficient learning algorithms under $s$-concave distributions. The new class of $s$-concave distributions is a broad and natural generalization of log-concavity, and includes many important additional distributions, e.g., the Pareto distribution and $t$-distribution.…

While the Matrix Generalized Inverse Gaussian ($\mathcal{MGIG}$) distribution arises naturally in some settings as a distribution over symmetric positive semi-definite matrices, certain key properties of the distribution and effective ways of sampling from the distribution have not been carefully studied. In this paper…

SGD converges to an invariant distribution with sub-Gaussian or sub-exponential properties.

We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each tradin…

Algorithm distinguishes light-tailed from non-light-tailed distributions.

In this paper, we present the results of Monte Carlo simulations for two popular techniques of long-range correlations detection - classical and modified rescaled range analyses. A focus is put on an effect of different distributional properties on an ability of the methods to efficiently distinguish between short and …

New HyperKahler structure found for 3-contact distributions on Sasakian manifolds.

The paper explores solutions to the distributional Bellman equation in reinforcement learning.

New method relaxes TV distance for two-sample testing without distributional assumptions.

ABROCA assesses algorithmic bias, revealing skewed distributions that inflate results.

This work evaluates graph models' robustness to structural distributional shifts.

Paper shows $L^\infty$-positivity and stochastic completeness are equivalent.

In this thesis, we study value distribution theoretical properties of the Gauss map of pseudo-algebraic minimal surfaces in n-dimensional Euclidean space. After reviewing basic facts, we give estimates for the number of exceptional values and the totally ramified value numbers and the corresponding unicity theorems for…

Paper tests DPPs for diversity models, distinguishing them from other distributions.

Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively and separate optimal estimators are known for each, in striking recent work, Ac…

We focus on the problem of how wealth is distributed among the units of a networked economic system. We first review the empirical results documenting that in many economies the wealth distribution is described by a combination of log--normal and power--law behaviours. We then focus on the Bouchaud--Mézard model of wea…

In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance, the European call-put parity corresponds to the central symmetry property, while…

We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the following problems: (1) Uniformity Testing: Testing whether all the $p_i$'s are …

A new framework assigns values to data points considering their distribution.

Aggregate network properties such as cluster cohesion and the number of bridge nodes can be used to glean insights about a network's community structure, spread of influence and the resilience of the network to faults. Efficiently computing network properties when the network is fully observed has received significant …

DECAF optimizes molecular graphs for ensemble properties, improving drug design accuracy.

New model predicts radiative properties of nanoparticle layers with high accuracy and uncertainty.

Diagonal transformations preserve independence structures in non-Gaussian distributions.

This work develops efficient methods for continuous-time distributional reinforcement learning.

New efficient algorithm for approximate PML distribution.

In this work, we introduce a novel probabilistic representation of deep learning, which provides an explicit explanation for the Deep Neural Networks (DNNs) in three aspects: (i) neurons define the energy of a Gibbs distribution; (ii) the hidden layers of DNNs formulate Gibbs distributions; and (iii) the whole architec…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size $k$ and desired…

Generative neural network designs novel 3D molecules with specified properties.

Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job m…