Related papers: Multiphase-Linear Ranking Functions and their Rela…
Functional data are frequently accompanied by a parametric template that describes the typical shapes of the functions. However, these parametric templates can incur significant bias, which undermines both utility and interpretability. To…
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…
Incomplete rankings on a set of items $\{1,\; \ldots,\; n\}$ are orderings of the form $a_{1}\prec\dots\prec a_{k}$, with $\{a_{1},\dots a_{k}\}\subset\{1,\dots,n\}$ and $k < n$. Though they arise in many modern applications, only a few…
Multiclass classification (MCC) is a fundamental machine learning problem of classifying each instance into one of a predefined set of classes. In the deep learning era, extensive efforts have been spent on developing more powerful neural…
A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…
The notion of \emph{rank} of a Boolean function has been a cornerstone in PAC learning theory, enabling quasipolynomial-time learning algorithms for polynomial-size decision trees. We present a novel characterization of rank, grounded in…
Fixed-point logic with rank (FPR) is an extension of fixed-point logic with counting (FPC) with operators for computing the rank of a matrix over a finite field. The expressive power of FPR properly extends that of FPC and is contained in…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Multi-label classification (MLC) is an important class of machine learning problems that come with a wide spectrum of applications, each demanding a possibly different evaluation criterion. When solving the MLC problems, we generally expect…
This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a compact and connected matrix Lie group without boundary, e.g. SO(n) and SE(n), in the presence of real-valued observations. This…
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
The classical theory of reinforcement learning (RL) has focused on tabular and linear representations of value functions. Further progress hinges on combining RL with modern function approximators such as kernel functions and deep neural…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
The last decade has seen a revolution in the theory and application of machine learning and pattern recognition. Through these advancements, variable ranking has emerged as an active and growing research area and it is now beginning to be…
We consider a multistage framework introduced recently where, given a time horizon t=1,2,...,T, the input is a sequence of instances of a (static) combinatorial optimization problem I_1,I_2,...,I_T, (one for each time step), and the goal is…
We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained,…