arXiv research

Recover manifold homology from a sample in Euclidean space.

The paper explores how to measure and optimize ad reach while maintaining user privacy.

The economy globalization measure problem is discussed. Four macroeconomic indices of twenty among the "richest" countries are examined. Four types of "distances" are calculated.Two types of networks are next constructed for each distance measure definition. It is shown that the globalization process can be best charac…

We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive $μ$-reach can be estimated by the same curvature measures of the offset of a compact set…

Various problems in manifold estimation make use of a quantity called the reach, denoted by $τ\_M$, which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. W…

New curvature measures characterize non-convex Wulff shapes in normed spaces.

Understanding the three-dimensional (3D) structure of the genome is essential for elucidating vital biological processes and their links to human disease. To determine how the genome folds within the nucleus, chromosome conformation capture methods such as HiC have recently been employed. However, computational methods…

AI progress measured by reduced compute needed to reach past performance.

Study shows how certain stochastic models reach a steady state over time.

We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of gene…

C-Learning estimates reachability over time to solve multi-goal tasks.

Study finds a non-locally contractible $r$-convex set.

We consider a new approach to portfolio selection in presence of transaction costs which allows to map the problem into one without costs. The proposed approach connects all the quantities of interest to exit times and probabilities to reach barriers. This leads to analytic results in the Wiener case and to directly me…

Study on sets with positive reach in Euclidean and Riemannian spaces.

Study calculates reach and curvature of a specific geometric variety.

Computes bounds on reach and r-convexity from point cloud data.

Study improves understanding of submanifold reach in Riemannian geometry.

Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization method for measures in Euclidean spaces and use it for reflecting underlying chan…

New complexity measure ADL connects to classical complexity measures.

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices …

Study non-Gaussian measures' concentration properties in metric spaces.

Paper estimates manifold reach using convexity defect function.

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology. When applying this to two case studies, accuracy exceeds alternative models wit…

Nilpotent groups can't be biLipschitz embedded into $L^1$.

We give new characterisations of sets of positive reach and show that a closed hypersurface has positive reach if and only if it is of class $C^{1,1}$. These results are then used to prove new alternating Steiner formulæ for hypersurfaces of positive reach. Furthermore, it will turn out that every hypersurface that sat…

Paper proposes a method to learn goal-reaching behaviors from scratch using imitation learning.

We determine the optimal strategy for investing in a Black-Scholes market in order to maximize the probability that wealth at death meets a bequest goal $b$, a type of goal-seeking problem, as pioneered by Dubins and Savage (1965, 1976). The individual consumes at a constant rate $c$, so the level of wealth required fo…

While reinforcement learning (RL) has the potential to enable robots to autonomously acquire a wide range of skills, in practice, RL usually requires manual, per-task engineering of reward functions, especially in real world settings where aspects of the environment needed to compute progress are not directly accessibl…

Diffusion reach probability between two nodes on a network is defined as the probability of a cascade originating from one node reaching to another node. An infinite number of cascades would enable calculation of true diffusion reach probabilities between any two nodes. However, there exists only a finite number of cas…

The paper extends submanifold reach to less regular $C^{1,α}$ classes.

A new optimizer DDC improves deep learning models by respecting symmetries.

Study shows spheres in high dimensions have maximum volume if they are smooth and have a specific reach.

Many problems in finance are related to first passage times. Among all of them, we chose three on which we contributed personally. Our first example relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way that tail events and core events contribute equally to the test (in the standard Kolmogorov-S…

We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.

Independent component analysis (ICA) is a method for recovering statistically independent signals from observations of unknown linear combinations of the sources. Some of the most accurate ICA decomposition methods require searching for the inverse transformation which minimizes different approximations of the Mutual I…

To understand the relationship between news sentiment and company stock price movements, and to better understand connectivity among companies, we define an algorithm for measuring sentiment-based network risk. The algorithm ranks companies in networks of co-occurrences, and measures sentiment-based risk, by calculatin…

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert--Schmidt norm of the cross-covariance operator) and transfer entrop…

We determine the optimal strategies for purchasing term life insurance and for investing in a risky financial market in order to maximize the probability of reaching a bequest goal while consuming from an investment account. We extend Bayraktar and Young (2015) by allowing the individual to purchase term life insurance…

Designing rewards for Reinforcement Learning (RL) is challenging because it needs to convey the desired task, be efficient to optimize, and be easy to compute. The latter is particularly problematic when applying RL to robotics, where detecting whether the desired configuration is reached might require considerable sup…

Two new estimators reduce costs and improve accuracy for EHR outcome prediction.

Study shows SNN graph Laplacians converge to k-NN graph Laplacians under large scale asymptotics.

Discuss folklore statements about manifolds with curvature bounds.

Paper proposes new Langevin samplers for sampling from log-concave distributions with superlinear gradient growth.

Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some mome…

Optimized parallel RNN training reaches up to 845x speedup.

The paper examines how background risk affects portfolio selection and optimal reinsurance design.

There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learn…

A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a GAN-based prior to solve linear inverse problems using projected gradient descent (…