arXiv research

In this paper, we study the confounder detection problem in the linear model, where the target variable $Y$ is predicted using its $n$ potential causes $X_n=(x_1,...,x_n)^T$. Based on an assumption of rotation invariant generating process of the model, recent study shows that the spectral measure induced by the regress…

Barren plateaus are not an average-case phenomenon, but a highly non-unique problem.

The paper analyzes Adam and SGD in nonstationary optimization, revealing tradeoffs between noise and drift.

A note proves the binary perceptron's capacity is less than 0.847.

Adaptive gradient methods such as Adam have been shown to be very effective for training deep neural networks (DNNs) by tracking the second moment of gradients to compute the individual learning rates. Differently from existing methods, we make use of the most recent first moment of gradients to compute the individual …

In this paper we will study the statistics of the unit geodesic flow normal to the boundary of a hyperbolic manifold with non-empty totally geodesic boundary. Viewing the time it takes this flow to hit the boundary as a random variable, we derive a formula for its moments in terms of the orthospectrum. The first moment…

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been sho…

We consider harmonic measures that arise from random walks on the mapping class group determined by probability distributions that have finite first moment with respect to the Teichmuller metric, and whose supports generate non-elementary subgroups. We prove that Teichmuller space with the Teichmuller metric is statist…

Random walks on hyperbolic spaces show linear growth in translation lengths.

Study resolvent convergence for random matrices with general covariance profiles.

Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on …

We consider random walks on the mapping class group that have finite first moment with respect to the word metric, whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichmuller geodesic is in the principal stratum of quadratic differentials. We show that a Teichmuller ge…

Paper shows robust generative learning with minimal assumptions on target distributions.

We model non-stationary volume-price distributions with a log-normal distribution and collect the time series of its two parameters. The time series of the two parameters are shown to be stationary and Markov-like and consequently can be modelled with Langevin equations, which are derived directly from their series of …

Random walk speed on Teichmüller space is a proper function.

This article presents a new model for demographic simulation which can be used to forecast and estimate the number of people in pension funds (contributors and retirees) as well as workers in a public institution. Furthermore, the model introduces opportunities to quantify the financial ows coming from future populatio…

Solves Christoffel-Minkowski problem and Hessian equations with radial symmetry.

This article presents an empirical study of thirteen derivative markets for commodity and financial assets. It compares the statistical properties of futures contracts's daily returns at different maturities, from 1998 to 2010 and for delivery dates up to 120 months. The analysis of the fourth first moments of the dist…

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the…

Study shows singularity of stationary measure on Furstenberg boundary for certain random walks.

Robust estimation under Huber's $ε$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth functions are impractical because of their computational intractability. In this paper, we est…

New EM algorithm improves deep generative network training.

Study uniform learnability of binary classification networks with communication.

Adapts safe policies for exploration in high-risk settings.

The paper develops methods for novelty detection on path space using signature-based statistics.

Given a measure on the Thurston boundary of Teichmueller space, one can pick a geodesic ray joining some basepoint to a randomly chosen point on the boundary. Different choices of measures may yield typical geodesics with different geometric properties. In particular, we consider two families of measures: the ones whic…

Randomly biased data makes complex models as easy to learn as simple ones.

This paper refines bounds on random walk speed in Teichmüller space.

Rod flow models Adam's behavior at the edge of stability.

Scale-free distributions and correlation functions found in financial data are reminiscent of the scale invariance of physical observables in the vicinity of a critical point. Here, we present empirical evidence for a transition phenomenon, accompanied by a symmetry breaking, in the investors' demand for stocks. We stu…

New methods target conditional demographic parity using optimal transport distances.

The paper offers a framework to analyze machine learning problems using concentration of measure.

New summary measures reveal geometric structure in weighted measures on manifolds.

Paper proposes robust risk measures for non-negative risks with partial information.

In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distrib…

MTAdam optimizes multiple loss terms in neural models, balancing gradients dynamically.

Paper proposes an efficient algorithm to handle high-order portfolio moments.

Optimal transport theory characterizes convex order between probability measures.

Study problem-dependent rates in statistical learning theory, achieving optimal generalization error bounds.

We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…

Modified EAT method improves Poisson gradient estimation.

The paper relaxes the stability condition to boost confidence in generalization for randomized learning algorithms.

In this paper we study iterative procedures for stationary equilibria in games with large number of players. Most of learning algorithms for games with continuous action spaces are limited to strict contraction best reply maps in which the Banach-Picard iteration converges with geometrical convergence rate. When the be…

Imputation-Powered Inference improves subpopulation efficiency in missing data settings.

Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each step, which is a simple multiplication between the inverse of the we…

Introduces TSI, a variance-based measure for persistence barcodes.

We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming th…

We study the column subset selection problem with respect to the entrywise $\ell_1$-norm loss. It is known that in the worst case, to obtain a good rank-$k$ approximation to a matrix, one needs an arbitrarily large $n^{Ω(1)}$ number of columns to obtain a $(1+ε)$-approximation to the best entrywise $\ell_1$-norm low ra…