Related papers: Hyper-sparse optimal aggregation
The paper outlines the principles of construction of a broad class of hierarchical aggregation algorithms of cluster analysis, essentially based on minimum distance mergers, which are derived from the general bi-partial objective function.…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
We consider the problem of aggregating the elements of a possibly infinite dictionary for building a decision procedure that aims at minimizing a given criterion. Along with the dictionary, an independent identically distributed training…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
Given a finite family of functions, the goal of model selection aggregation is to construct a procedure that mimics the function from this family that is the closest to an unknown regression function. More precisely, we consider a general…
For massive data stored at multiple machines, we propose a distributed subsampling procedure for the composite quantile regression. By establishing the consistency and asymptotic normality of the composite quantile regression estimator from…
Massive data bring the big challenges of memory and computation for analysis. These challenges can be tackled by taking subsamples from the full data as a surrogate. For functional data, it is common to collect multiple measurements over…
This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…
Nowadays, several crowdsourcing projects exploit social choice methods for computing an aggregate ranking of alternatives given individual rankings provided by workers. Motivated by such systems, we consider a setting where each worker is…
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition and the anchored decomposition are typical techniques to find…
There are many problems in machine learning and data mining which are equivalent to selecting a non-redundant, high "quality" set of objects. Recommender systems, feature selection, and data summarization are among many applications of…
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…
This paper addresses a problem of estimating an additive functional given $n$ i.i.d. samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size $k$. The additive functional is defined as…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over $\operatorname…
In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world…
This paper considers the problem of clustering a partially observed unweighted graph---i.e., one where for some node pairs we know there is an edge between them, for some others we know there is no edge, and for the remaining we do not know…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…