Related papers: Splitting Localization and Prediction Numbers

Predict-then-Optimize is a framework for using machine learning to perform decision-making under uncertainty. The central research question it asks is, "How can the structure of a decision-making task be used to tailor ML models for that…

Identifiability, and the closely related idea of partial smoothness, unify classical active set methods and more general notions of solution structure. Diverse optimization algorithms generate iterates in discrete time that are eventually…

The connection between dependency trees and spanning trees is exploited by the NLP community to train and to decode graph-based dependency parsers. However, the NLP literature has missed an important difference between the two structures:…

In this paper we analyze a hash function for $k$-partitioning a set into bins, obtaining strong concentration bounds for standard algorithms combining statistics from each bin. This generic method was originally introduced by Flajolet and…

We propose a modification that corrects for split-improvement variable importance measures in Random Forests and other tree-based methods. These methods have been shown to be biased towards increasing the importance of features with more…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Problem 1.5.7 from Pitman's Saint-Flour lecture notes: Does there exist for each n a fragmentation process (\Pi_{n,k}, 1 \leq k \leq n) taking values in the space of partitions of {1,2,...,n} such that \Pi_{n,k} is distributed like the…

We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-constructive arguments show that F is satisfiable for clause/variable ratios m/n< r(k)~2^k ln 2 with high probability. Yet no efficient algorithm is…

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…

Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…

Starting from a discussion of the concrete representations of the coordinates of the k-Minkowski spacetime (in 1+1 dimensions, for simplicity), we explicitly compute the associated Weyl operators as functions of a pair of Schroedinger…

We initiate a novel approach to explain the predictions and out of sample performance of random forest (RF) regression and classification models by exploiting the fact that any RF can be mathematically formulated as an adaptive weighted K…

We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the…

We consider a Galton-Watson tree where each node is marked independently of each others with a probability depending on itsout-degree. Using a penalization method, we exhibit new martingales where the number of marks up to level n -- 1…

Plucking polynomial of a plane rooted tree with a delay function $\alpha$ was introduced in 2014 by J.H.~Przytycki. As shown in this paper, plucking polynomial factors when $\alpha$ satisfies additional conditions. We use this result and…

With recent developments in remote sensing technologies, plot-level forest resources can be predicted utilizing airborne laser scanning (ALS). The prediction is often assisted by mostly vertical summaries of the ALS point clouds. We present…

Gorman and Bedrick (2019) argued for using random splits rather than standard splits in NLP experiments. We argue that random splits, like standard splits, lead to overly optimistic performance estimates. We can also split data in biased or…