arXiv research

A random walk $w_n$ on a separable, geodesic hyperbolic metric space $X$ converges to the boundary $\partial X$ with probability one when the step distribution supports two independent loxodromics. In particular, the random walk makes positive linear progress. Progress is known to be linear with exponential decay when …

We show that a random walk on the mapping class group of an orientable surface of finite type makes linear progress in the relative metric, which is quasi-isometric to the complex of curves.

Linear progress observed in fibered 3-manifold embeddings.

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new ec…

Study uses machine learning and survival analysis to predict CKD progression.

First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. W…

We develop an algorithm for systematic design of a large artificial neural network using a progression property. We find that some non-linear functions, such as the rectifier linear unit and its derivatives, hold the property. The systematic design addresses the choice of network size and regularization of parameters. …

We introduce a novel approach for predicting the progression of adolescent idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray images. Recent progress in machine learning have allowed to improve classification and prognosis rates, but lack a probabilistic framework to measure uncertainty in the …

Modeling disease progression in healthcare administrative databases is complicated by the fact that patients are observed only at irregular intervals when they seek healthcare services. In a longitudinal cohort of 76,888 patients with chronic obstructive pulmonary disease (COPD), we used a continuous-time hidden Markov…

Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization (out-of-samples), and cost-effectiveness (linearization). To this end, a novel linearized subsp…

Arguably, unsupervised learning plays a crucial role in the majority of algorithms for processing brain imaging. A recently introduced unsupervised approach Deep InfoMax (DIM) is a promising tool for exploring brain structure in a flexible non-linear way. In this paper, we investigate the use of variants of DIM in a se…

Stochastic approximation algorithms show exponential progress bounds.

This paper explains a mechanism called phase collapse that improves image classification accuracy.

Jump Markov linear models consists of a finite number of linear state space models and a discrete variable encoding the jumps (or switches) between the different linear models. Identifying jump Markov linear models makes for a challenging problem lacking an analytical solution. We derive a new expectation maximization …

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence guarantees and optimal estimation accuracy in high dimensions. We further extend the …

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of data-representations, i.e. the minimal number of parameters needed to describe a represent…

There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning of LDS. We present an approach to proper learning of LDS, which in spite of the …

By reducing optimization to a sequence of smaller subproblems, working set algorithms achieve fast convergence times for many machine learning problems. Despite such performance, working set implementations often resort to heuristics to determine subproblem size, makeup, and stopping criteria. We propose BlitzWS, a wor…

Variance reduced stochastic gradient (SGD) methods converge significantly faster than the vanilla SGD counterpart. However, these methods are not very practical on large scale problems, as they either i) require frequent passes over the full data to recompute gradients---without making any progress during this time (li…

In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsific…

Motivated by drug design, we consider the best-arm identification problem in generalized linear bandits. More specifically, we assume each arm has a vector of covariates, there is an unknown vector of parameters that is common across the arms, and a generalized linear model captures the dependence of rewards on the cov…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature mapping, they are still subject to cubic cost on the number of points. Given only …

Supervised linear feature extraction can be achieved by fitting a reduced rank multivariate model. This paper studies rank penalized and rank constrained vector generalized linear models. From the perspective of thresholding rules, we build a framework for fitting singular value penalized models and use it for feature …

It is widely believed that the success of deep convolutional networks is based on progressively discarding uninformative variability about the input with respect to the problem at hand. This is supported empirically by the difficulty of recovering images from their hidden representations, in most commonly used network …

We study the error landscape of deep linear and nonlinear neural networks with the squared error loss. Minimizing the loss of a deep linear neural network is a nonconvex problem, and despite recent progress, our understanding of this loss surface is still incomplete. For deep linear networks, we present necessary and s…

Despite their popularity, many questions about the algebraic constraints imposed by linear structural equation models remain open problems. For causal discovery, two of these problems are especially important: the enumeration of the constraints imposed by a model, and deciding whether two graphs define the same statist…

In previous work, the authors studied the linear stability of algebraic Ricci solitons on simply connected solvable Lie groups (solvsolitons), which are stationary solutions of a certain normalization of Ricci flow. Many examples were shown to be linearly stable, leading to the conjecture that all solvsolitons are line…

Deep networks achieve linear separability through progressive folding of data in higher dimensions.

While a lot of progress has been made in recent years, the dynamics of learning in deep nonlinear neural networks remain to this day largely misunderstood. In this work, we study the case of binary classification and prove various properties of learning in such networks under strong assumptions such as linear separabil…

Paper develops efficient RL algorithm for general value function approximation.

Sign information is the key to overcoming the inevitable saturation error in compressive sensing systems, which causes information loss and results in bias. For sparse signal recovery from saturation, we propose to use a linear loss to improve the effectiveness from existing methods that utilize hard constraints/hinge …

Transformers improve Alzheimer's disease progression prediction by accounting for irregular biomarker histories.

Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the rôle played by piecewise affine and convex nonlinearities like the ReLU and absolute value …

Let G be a countable group which acts by isometries on a separable, but not necessarily proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G contains two independent hyperbolic isometries. We show that a random walk on such G converges to the Gromov boundary almost surely. We apply the co…

Industry evolution caused by various reasons, among which technology progress driving industry development has been approved, but with the new trend of industry convergence, inter-industry convergence also plays an increasing important role. This paper plans to probe the industry synergetic evolution mechanism based on…

Paper introduces a new curriculum generation method for reinforcement learning.

Lie groups applied to tech progress in economic growth.

This paper improves disentanglement in VAEs by progressively learning hierarchical representations.

Bayesian model identifies health disparities in disease progression.

New algorithm outperforms existing ones by focusing on mastering rate.

The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adju…

In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in its primitive length spectrum. Moreover, we show the stronger property that every primitive length occurs in arbitrarily long arithmetic progr…

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider…

This paper analyzes generalization for linear models with spiked covariance structures.

Cohen et al. (2021) show GD trajectories align on a bifurcation diagram.

Linear classifiers can resist adversarial attacks on Gaussian data.

The concept of progress has characterized human society from millennia. However, this concept is elusive and too often given for certain. The goal of this paper is to suggest a general definition of human progress that satisfies, whenever possible the conditions of independence, generality, epistemological applicabilit…

Survey of recent progress in Sasakian geometry.