arXiv research

This paper models stock prices using a Janardan Galton Watson process.

The paper explores statistical limits for detecting correlation in tree structures.

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitra…

Random hyperbolic surfaces with punctures converge to the Brownian sphere.

The purpose of this paper is to design an algorithm for the computation of the counterparty risk which is competitive in regards of a brute force "Monte-Carlo of Monte-Carlo" method (with nested simulations). This is achieved using marked branching diffusions describing a Galton-Watson random tree. Such an algorithm le…

Ensemble learning is a statistical paradigm built on the premise that many weak learners can perform exceptionally well when deployed collectively. The BART method of Chipman et al. (2010) is a prominent example of Bayesian ensemble learning, where each learner is a tree. Due to its impressive performance, BART has rec…

A study on the depth of graph neural networks on sparse graphs, revealing a dichotomy based on the Kesten-Stigum ratio.

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic n…

Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing --and yet poorly understood-- dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even sophisticated semi-definite programming (SDP) relaxations fail. In order to explore this p…

This note provides an error bound for the Hartman-Watson integral's leading term.

A new method TNW-CATE estimates treatment effects using neural networks.

This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential functionals of Brownian motion have been studied in terms of …

Barrieu, Rouault, and Yor [J. Appl. Probab. 41 (2004)] determined asymptotics for the logarithm of the distribution function of the Hartman-Watson distribution. We determine the asymptotics of the density. This refinement can be applied to the pricing of Asian options in the Black-Scholes model.

Paper provides an upper bound for bias of Nadaraya-Watson kernel regression.

New insights into Nadaraya-Watson interpolators show varied generalization behaviors.

We show that any exceptional non-trivial Dehn surgery on a twist knot, except the trefoil, yields a 3-manifold whose fundamental group is left-orderable. This is a generalization of a result of Clay, Lidman and Watson, and also gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as wel…

Authors derive the first two terms of the Hartman-Watson distribution's expansion for small t.

We prove that the link of a complex normal surface singularity is an L--space if and only if the singularity is rational. This via a recent result of Hanselman, J. Rasmussen, S. D. Rasmussen and Watson (proving the conjecture of Boyer, Gordon and Watson), shows that a singularity link is not rational if and only if its…

Paper develops NW kernel estimator for LSPs with Wasserstein bounds.

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since large classes of L-spaces can be produced from Dehn surgery on knots in the 3-sphere, it is natural to ask what conditions on the knot group are suffi…

A new loss function for VAEs improves image quality and efficiency.

New insights into simple kernel smoothing reveal surprising asymptotics.

It has been recently conjectured by Boyer-Gordon-Watson that a closed, orientable, irreducible $3$-manifold $M$ is a Heegaard Floer $L$-space if and only if $π_1(M)$ is not left-orderable. In this article, we study this conjecture from the point of view of lattice cohomology, an invariant introduced by Némethi which is…

Estimates time-series drifts from i.i.d. data using a direct Nadaraya-Watson plug-in method.

Using an invariant defined by Rasmussen, we extend an argument given by Hedden and Watson which further restricts which Alexander polynomials can be realized by $L$-space knots.

Study finds a small correction to Asian option volatility.

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large families of L-spaces, it is natural to examine the conjecture on these 3-manifolds. Greene, Lewalle…

Improved local feature attributions using neighbourhood reference distributions.

We show that any exceptional non-trivial Dehn surgery on a hyperbolic two-bridge knot yields a 3-manifold whose fundamental group is left-orderable. This gives a new supporting evidence for a conjecture of Boyer, Gordon and Watson.

The paper introduces a method to quantify uncertainty in neural networks without parametric assumptions.

Let L \subset S^3 denote an alternating link and Sigma(L) its branched double-cover. We give a short proof of the fact that the fundamental group of Sigma(L) admits a left-ordering iff L is an unlink. This result is originally due to Boyer-Gordon-Watson.

A new polynomial invariant for strongly involutive links.

Generative models use kernel smoothing for conditioning on small example sets.

Study on predicting graph labels at nodes using local averaging and distance estimation.

We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples. Truncated samples from a $d$-variate normal ${\cal N}(\mathbfμ,\mathbfΣ)$ means a samples is only re…

Efficient classifier with uncertainty bounds for safety-critical applications.

We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite mixture representation, which allows the orientation parameter to be estimated u…

TAP transfers knowledge from unlabeled data to improve cross-modal learning.

This study improves estimation of locally stationary functional time series using NW method.

We show that the resulting manifold by $r$-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope $r$ satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson that relates $L$-spaces and the left-orderability of their funda…

ABIForest improves anomaly detection using attention weights.

New theory shows how multi-head attention reduces variance and decorrelates outputs.

We show that the fundamental group of the double branched cover of an infinite family of homologically thin, non-quasi-alternating knots is not left-orderable, giving further support for a conjecture of Boyer, Gordon, and Watson that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental…

This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of intermittent dynamics generating power law distributions. Using insights on the beha…

Transformers can approximate Kalman Filtering in linear systems with small error.

Motivated by Clay and Watson's question on left-orderability of the fundamental group of the resultant space of an $r'$-surgery on the $(p, q)$-cable knots for $r' \in (pq-p-q,pq)$, this paper proves by elementary means that for specific pairs of $(p,q)$-cable knots of torus knots, $r' \in [pq-1,pq]$ gives a surgery yi…

Enhances supervised learning speed with KT algorithm.