arXiv research

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

The paper derives inequalities for Riemannian maps and submersions involving quaternionic space forms.

OLLA framework efficiently samples from constrained distributions with nonconvex constraints.

TAET tackles long-tailed distributions in adversarial robustness.

We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …

In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result are also considered.

General equilibrium equations in economics play the same role with many-body Newtonian equations in physics. Accordingly, each solution of the general equilibrium equations can be regarded as a possible microstate of the economic system. Since Arrow's Impossibility Theorem and Rawls' principle of social fairness will p…

Model shows significant income inequality emerges from equal opportunities in a simple economy.

Study proves topological complexity and LS-category inequalities for specific groups and manifolds.

The distributional category bounds manifold invariants and imposes constraints.

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 …

The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result regarding the relationship between distributional robustness and regularisation, as…

Paper finds robust $Λ$-quantiles equal to extremal distributions.

We investigate the relation between economic growth and equality in a modified version of the agent-based asset exchange model (AEM). The modified model is a driven system that for a range of parameter space is effectively ergodic in the limit of an infinite system. We find that the belief that "a rising tide lifts all…

Estimates returns for dollar cost averaging using geometric Brownian motion.

ELBO converges to a sum of entropies for many generative models.

New measures generalize existing ones, linking information and risk.

In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By var…

We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a generalization of the maximum mean discrepancy tests described in Gretton et al. [2006], …

New method uses causal thinking to make AI fairer decisions.

New research shows unlabeled data is equally valuable as labeled data in certain semi-supervised learning scenarios.

New insights into noise distribution for self-supervised learning.

There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson's case, testing the equality…

An important factor to guarantee a fair use of data-driven recommendation systems is that we should be able to communicate their uncertainty to decision makers. This can be accomplished by constructing prediction intervals, which provide an intuitive measure of the limits of predictive performance. To support equitable…

Proposes a fair classification model using Wasserstein ambiguity sets.

We study an online classification problem with partial feedback in which individuals arrive one at a time from a fixed but unknown distribution, and must be classified as positive or negative. Our algorithm only observes the true label of an individual if they are given a positive classification. This setting captures …

Paper studies PSGD for constrained optimization problems and its statistical properties.

This paper constructs Brownian motion on complex flag manifolds and finds joint distribution of stochastic areas.

We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipf's law; that is, it can be approximated by a …

We investigate the Japanese personal income distribution in the high income range over the 112 years 1887-1998, and that in the middle income range over the 44 years 1955-98. It is observed that the distribution pattern of the lognormal with power law tail is the universal structure. However the indexes specifying the …

We study the interplay between sequential decision making and avoiding discrimination against protected groups, when examples arrive online and do not follow distributional assumptions. We consider the most basic extension of classical online learning: "Given a class of predictors that are individually non-discriminato…

FaiREE provides fair classification with guarantees for small datasets.

Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level. Current approaches, however, do not propagate the uncertainty in observations due to sampling variability in the gr…

This paper finds a unique partition of a sample space for estimating continuous distributions.

Consider a reference Markov process with initial distribution $π_{0}$ and transition kernels $\{M_{t}\}_{t\in[1:T]}$, for some $T\in\mathbb{N}$. Assume that you are given distribution $π_{T}$, which is not equal to the marginal distribution of the reference process at time $T$. In this scenario, Schrödinger addressed t…

Proves weak convergence equals mean convergence in GGC.

In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…

This work examines the sensitivity of energy distance to mean differences compared to covariance differences.

The paper sets new bounds for Ricci-curvature in submersions and maps.

New rank 3 distributions with exponentially growing symmetries.

A new tail-shape index based on Value at Risk and Expected Shortfall.

To make decisions based on a model fit with auto-encoding variational Bayes (AEVB), practitioners often let the variational distribution serve as a surrogate for the posterior distribution. This approach yields biased estimates of the expected risk, and therefore leads to poor decisions for two reasons. First, the mode…

Bayesian method recovers causal structure in SEMs with equal error variances.

This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents in payment for goods and services. Starting from the initially equal distrib…

We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact structure on a closed 3-dimensional manifold $M$ there is a metric, such that th…

We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data p…

A non-trivial predictor satisfies demographic parity and equalizes group risks in regression.