arXiv research

This paper proposes a method to approximate non-Gaussian likelihoods in Gaussian Processes.

This paper extends depth separation results to piece-wise oscillatory functions.

We show how neural models can be used to realize piece-wise constant functions such as decision trees. The proposed architecture, which we call locally constant networks, builds on ReLU networks that are piece-wise linear and hence their associated gradients with respect to the inputs are locally constant. We formally …

Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes affect the prediction is critical to users. However, most, if not all, existing ordi…

This work focuses on the estimation of multiple change-points in a time-varying Ising model that evolves piece-wise constantly. The aim is to identify both the moments at which significant changes occur in the Ising model, as well as the underlying graph structures. For this purpose, we propose to estimate the neighbor…

We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a family of models indexed over the collection of partitions of the design points and…

In this survey article, we review the relation between heat kernels and path integrals. In particular, we review recent results on the approximation of the Wiener measure on compact manifold by measures on (finite-dimensional) spaces of piece-wise geodesics.

Optimal order execution strategies for brokers under reference benchmarks.

In this paper we analyze the asymptotic properties of l1 penalized maximum likelihood estimation of signals with piece-wise constant mean values and/or variances. The focus is on segmentation of a non-stationary time series with respect to changes in these model parameters. This change point detection and estimation pr…

This work simplifies adversarial attacks using neural networks, reducing computation and improving training convergence.

RUMBoost combines RUMs and deep learning for better choice modelling.

PyChEst detects changes in non-stationary time series without distributional assumptions.

We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points. In particular, consider a twice differentiable (non-convex) objective function whose gradient has Lipschitz constant L and whose Hessian is well-behaved. We prove that the probability of init…

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. Th…

Study tackles inverse problems on low-dimensional manifolds, proving stability and proposing a reconstruction algorithm.

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…

The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.

Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima -- at least those discovered by gradient-based optimization -- turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segm…

In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus correlation analysis, which is only optimal in case of linear dependencies. First, w…

In this paper, we investigate a transition from an elastica to a piece-wised elastica whose connected point defines the hinge angle $φ_0$; we refer the piece-wised elastica $Λ_{φ_0}$-elastica or $Λ$-elastica. The transition appears in the bending beam experiment; we compress elastic beams gradually and then suddenly du…

We consider billiard ball motion in a convex domain of the Euclidean plane bounded by a piece-wise smooth curve influenced by the constant magnetic field. We show that if there exists a polynomial in velocities integral of the magnetic billiard flow then every smooth piece $γ$ of the boundary must be algebraic and eith…

AdaPID optimizes diffusion-based samplers by dynamically adjusting schedules.

DAMI uses interpretable regions to select informative samples for deep learning models.

CTR prediction in real-world business is a difficult machine learning problem with large scale nonlinear sparse data. In this paper, we introduce an industrial strength solution with model named Large Scale Piece-wise Linear Model (LS-PLM). We formulate the learning problem with $L_1$ and $L_{2,1}$ regularizers, leadin…

Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is however piece-wise constant (the sorting permutation of a vector does not change if th…

We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely consid…

A new method for creating simpler models from complex ones.

We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for ge…

Modern neural network training relies on piece-wise (sub-)differentiable functions in order to use backpropagation to update model parameters. In this work, we introduce a novel method to allow simple non-differentiable functions at intermediary layers of deep neural networks. We do so by training with a differentiable…

Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.

UNIPoint universally approximates point process intensities.

Deep neural networks paved the way for significant improvements in image visual categorization during the last years. However, even though the tasks are highly varying, differing in complexity and difficulty, existing solutions mostly build on the same architectural decisions. This also applies to the selection of acti…

Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study…

Considering Wirtinger's inequality for piece-wise equipartite functions we find a discrete version of this classical inequality. The main tool we use is the theorem of classification of isometries. Our approach provides a new elementary proof of Wirtinger's inequality that also allows to study the case of equality. Mor…

The paper proves Sard's theorem for polynomial maps in infinite dimensions.

Assessing world-wide financial integration constitutes a recurrent challenge in macroeconometrics, often addressed by visual inspections searching for data patterns. Econophysics literature enables us to build complementary, data-driven measures of financial integration using graphs. The present contribution investigat…

Method to create rational Seifert surfaces for knots in Lens space.

It is shown that most of the well-known basic results for Sobolev-Slobodeckii and Bessel potential spaces, known to hold on bounded smooth domains in $\mathbb{R}^n$, continue to be valid on a wide class of Riemannian manifolds with singularities and boundary, provided suitable weights, which reflect the nature of the s…

Let S be a triangulated 2-sphere with fixed triangulation T. We apply the methods of thin position from knot theory to obtain a simple version of the three geodesics theorem for the 2-sphere [5]. In general these three geodesics may be unstable, corresponding, for example, to the three equators of an ellipsoid. Using a…

Given two points on a soup can or conical cup with lid, we find and classify all paths of minimal length connecting them. When the number of minimal paths is finite, there are at most four on a can and three on a cup. At worst, minimal paths are piece-wise smooth with three components, each of which is a classical geod…

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is ma…

Regularization is typically understood as improving generalization by altering the landscape of local extrema to which the model eventually converges. Deep neural networks (DNNs), however, challenge this view: We show that removing regularization after an initial transient period has little effect on generalization, ev…

New framework optimizes classification trees with logistic loss and $\ell_1$ regularization.

This paper accelerates TV regularization algorithms by unrolling proximal gradient descent.

A new algorithm finds optimal solutions for constrained decision processes.

We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants on smooth surfaces with smooth boundaries. The differences to the smooth case a…

Study Whittle index learning algorithms for restless bandits with constant stepsizes.

Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.