A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.
New DKPP family controls positive and negative dependence in random subsets.
Characterizes symmetric Bernoulli distributions with minimal convex sums.
PAM models generate dependent random distributions across groups with overlapping clusters.
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-Rényi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respec…
A new copula, the checkerboard copula, maximizes entropy and preserves dependence.
Unexpectedly, weighted Pareto variables are stochastically dominant.
Random features provide a practical framework for large-scale kernel approximation and supervised learning. It has been shown that data-dependent sampling of random features using leverage scores can significantly reduce the number of features required to achieve optimal learning bounds. Leverage scores introduce an op…
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
Deep learning depends on tuning layers near critical points.
CMRFs extend PGMs for topological data, capturing both conditional and marginal dependencies.
We present DUAL-LOCO, a communication-efficient algorithm for distributed statistical estimation. DUAL-LOCO assumes that the data is distributed according to the features rather than the samples. It requires only a single round of communication where low-dimensional random projections are used to approximate the depend…
The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric. Given suitable restrictions on the genus of the surface, we consider the number…
Study tail risk aggregation under dependence uncertainty.
Generative moment matching networks (GMMNs) are introduced for generating quasi-random samples from multivariate models with any underlying copula in order to compute estimates under variance reduction. So far, quasi-random sampling for multivariate distributions required a careful design, exploiting specific propertie…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the posterior distribution are shared amongst groups, and hence groups can borrow informatio…
Diversification improves profits for heavy-tailed investments.
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance…
We revisit the Kolmogorov-Smirnov and Cramér-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the "effective" number of independent observations. The generalised GoF tests are not…
Representations based on random walks can exploit discrete data distributions for clustering and classification. We extend such representations from discrete to continuous distributions. Transition probabilities are now calculated using a diffusion equation with a diffusion coefficient that inversely depends on the dat…
New algorithm speeds up MCMC for complex distributions.
Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying finite-area Riemann surfaces associated with random cubic graphs; b…
New tree-structured Markov fields with Poisson marginals for counting variables.
Domain randomization (DR) is a successful technique for learning robust policies for robot systems, when the dynamics of the target robot system are unknown. The success of policies trained with domain randomization however, is highly dependent on the correct selection of the randomization distribution. The majority of…
Innovative extensions to option pricing models using asymmetric Brownian motion and random walk approaches.
Proposes logistic-beta process for modeling dependent probabilities with beta marginals.
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
The randomized-feature approach has been successfully employed in large-scale kernel approximation and supervised learning. The distribution from which the random features are drawn impacts the number of features required to efficiently perform a learning task. Recently, it has been shown that employing data-dependent …
A novel algorithm minimizes regret in a multi-agent bandit problem with time-varying random graphs and heterogeneous rewards.
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We derive also the information geometry of the 3-manifold of McKay bivariate gamma dist…
Study on lengths of random multicurves on hyperbolic surfaces.
The paper provides bounds on the CDF of a variable under nonstationary conditions.
GMMNs model cross-sectional dependence for better option pricing and simulation.
In recent studies, the generalization properties for distributed learning and random features assumed the existence of the target concept over the hypothesis space. However, this strict condition is not applicable to the more common non-attainable case. In this paper, using refined proof techniques, we first extend the…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function , consistent estimators of the mean embedding of a random variable lead to consistent estimators of the mean embedding of . For Matérn ke…
Paper proposes a generalized precision matrix for t-Student distributions to improve portfolio optimization.
Quantitative CLTs show neural network distributions converge to Gaussian as width increases.
We present a methodology for clustering N objects which are described by multivariate time series, i.e. several sequences of real-valued random variables. This clustering methodology leverages copulas which are distributions encoding the dependence structure between several random variables. To take fully into account …
We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the …
Paper develops online statistical inference methods for stochastic optimization using Kiefer-Wolfowitz algorithms.
The paper proves a distribution claim for neural network Jacobians.
The covariance graph (aka bi-directed graph) of a probability distribution is the undirected graph where two nodes are adjacent iff their corresponding random variables are marginally dependent in . In this paper, we present a graphical criterion for reading dependencies from , under the assumption that $…
Generative model for joint discrete distributions using randomized assignment flows.
In this paper, we study the stochastic combinatorial multi-armed bandit (CMAB) framework that allows a general nonlinear reward function, whose expected value may not depend only on the means of the input random variables but possibly on the entire distributions of these variables. Our framework enables a much larger c…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the collective risk model, where the total claim size in a portfolio is the sum of a …
Fermat-Torricelli points help assess investment risks by smoothing series data.
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
Estimates copula density for complex data distributions.