Related papers: Monotone Curve Estimation via Convex Duality
We discuss two novel approaches to the classical two-sample problem. Our starting point are properly standardized and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic…
A significant problem with most functional data analyses is that of misaligned curves. Without adjustment, even an analysis as simple as estimation of the mean will fail. One common method to synchronize a set of curves involves equating…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
Exact subgraph matching is a fundamental graph operator that supports many graph analytics tasks, yet it remains computationally challenging due to its NP-completeness. Recent learning-based approaches accelerate query processing via…
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates.…
We study prior-independent pricing for selling a single item to a single buyer when the seller observes only a single sample from the valuation distribution, while the buyer knows the distribution. Classical robust pricing approaches either…
This paper fills the limited statistical understanding of Shapley values as a variable importance measure from a nonparametric (or smoothing) perspective. We introduce population-level \textit{Shapley curves} to measure the true variable…
We propose a kernel-based nonparametric framework for mean-variance optimization that enables inference on economically motivated shape constraints in finance, including positivity, monotonicity, and convexity. Many central hypotheses in…
In this paper we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed convex sets. The proposed…
Shape constrained regression analysis has applications in dose-response modeling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
We present a generic solution to the fundamental problem of how to connect two points in a plane by a smooth curve that goes through these points with a given slope. The smoothness of any curve depends both on its curvature and its length.…
Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…