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An aesthetics evaluation model is at the heart of predicting users' aesthetic experience and developing user interfaces with higher quality. However, previous methods on aesthetic evaluation largely ignore the interpretability of the model…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
An important factor in the practical implementation of optimization models is the acceptance by the intended users. This is influenced among other factors by the interpretability of the solution process. Decision rules that meet this…
Operating systems are currently viewed ostensively. As a result they mean different things to different people. The ostensive character makes it is hard to understand OSes formally. An intensional view can enable better formal work, and…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
Over the last fifteen years, web searching has seen tremendous improvements. Starting from a nearly random collection of matching pages in 1995, today, search engines tend to satisfy the user's informational need on well-formulated queries.…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
High-dimensional feature vectors are likely to contain sets of measurements that are approximate replicates of one another. In complex applications, or automated data collection, these feature sets are not known a priori, and need to be…
We are often interested in decomposing complex, structured data into simple components that explain the data. The linear version of this problem is well-studied as dictionary learning and factor analysis. In this work, we propose a…
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, such problems are typically tackled…
Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to…
The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…
We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…
In this paper, we consider approximations of principal component projection (PCP) without explicitly computing principal components. This problem has been studied in several recent works. The main feature of existing approaches is viewing…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…
The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas…
Classifying images with an interpretable decision-making process is a long-standing problem in computer vision. In recent years, Prototypical Part Networks has gained traction as an approach for self-explainable neural networks, due to…
Interpretability is becoming increasingly important for predictive model analysis. Unfortunately, as remarked by many authors, there is still no consensus regarding this notion. The goal of this paper is to propose the definition of a score…
In this paper we propose a new approach to study the properties of the Partial Least Squares (PLS) estimator. This approach relies on the link between PLS and discrete orthogonal polynomials. Indeed many important PLS objects can be…