arXiv research

The paper studies continuous submodular functions and their optimization.

New algorithms solve DR-submodular maximization with faster convergence.

SGD improves DR by solving two-stage sampling problems.

In this paper, we study a certain class of online optimization problems, where the goal is to maximize a function that is not necessarily concave and satisfies the Diminishing Returns (DR) property under budget constraints. We analyze a primal-dual algorithm, called the Generalized Sequential algorithm, and we obtain t…

DR-submodular continuous functions are important objectives with wide real-world applications spanning MAP inference in determinantal point processes (DPPs), and mean-field inference for probabilistic submodular models, amongst others. DR-submodularity captures a subclass of non-convex functions that enables both exact…

A new DR formulation improves metric learning for faster and more stable performance.

Paper presents ERM with $f$-divergence regularization and its properties.

Off-policy evaluation (OPE) in both contextual bandits and reinforcement learning allows one to evaluate novel decision policies without needing to conduct exploration, which is often costly or otherwise infeasible. The problem's importance has attracted many proposed solutions, including importance sampling (IS), self…

Paper proposes methods to reduce bias and variance in recommender systems.

Let $(M, \dr M)$ be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that $\dr M$ looks locally like a hyperideal polyhedron, and we characterize the possible dihedral angles. We find as special cases the results of Bao and Bonah…

This paper establishes non-asymptotic learning bounds for the DR covariate shift adaptation.

FEALM learns features for better nonlinear DR of hidden patterns.

DR-MCTS improves decision quality and sample efficiency in complex environments.

The paper improves DR estimators for off-policy evaluation in contextual bandits.

Paper improves $\ell^{0}$-SSC for noisy data by proving SDP and proposing Noisy-DR-$\ell^{0}$-SSC.

Let $X=\mathbf{X}\cup\mathbf{Z}$ be a data set in $\mathbb{R}^D$, where $\mathbf{X}$ is the training set and $\mathbf{Z}$ is the test one. Many unsupervised learning algorithms based on kernel methods have been developed to provide dimensionality reduction (DR) embedding for a given training set $Φ: \mathbf{X} \to \mat…

New DR-IC estimator reduces bias and variance in OPE.

Paper defines and evaluates DR complex for persistent homology.

Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version).…

Dimensionality reduction (DR) is often used as a preprocessing step in classification, but usually one first fixes the DR mapping, possibly using label information, and then learns a classifier (a filter approach). Best performance would be obtained by optimizing the classification error jointly over DR mapping and cla…

Let $(M, \partial M)$ be a compact 3-manifold with boundary, which admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on $M$ such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature $K>-1$, and that the th…

New DR method improves robustness in high-dimensional treatment effects.

Over the past few decades, we have witnessed a large family of algorithms that have been designed to provide different solutions to the problem of dimensionality reduction (DR). The DR is an essential tool to excavate the important information from the high-dimensional data by mapping the data to a low-dimensional subs…

Interactive DR framework for comparing datasets.

New model-free DR-RL algorithm with finite sample complexity.

The bag of words (BOW) represents a corpus in a matrix whose elements are the frequency of words. However, each row in the matrix is a very high-dimensional sparse vector. Dimension reduction (DR) is a popular method to address sparsity and high-dimensionality issues. Among different strategies to develop DR method, Un…

Paper tackles online learning for DR management with incentives.

We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the…

New DR algorithm preserves both local and global structure.

In this paper, we propose a novel recurrent neural network architecture for speech separation. This architecture is constructed by unfolding the iterations of a sequential iterative soft-thresholding algorithm (ISTA) that solves the optimization problem for sparse nonnegative matrix factorization (NMF) of spectrograms.…

New dual formulation reduces generalization error for ERM-fDR.

We study the behaviour of analytic torsion under smooth fibrations. Namely, let F \to E \to^{f} B be a smooth fiber bundle of connected closed oriented smooth manifolds and let $V$ be a flat vector bundle over $E$. Assume that $E$ and $B$ come with Riemannian metrics and $V$ comes with a unimodular (not necessarily fla…

Training of deep models for classification tasks is hindered by local minima problems and vanishing gradients, while unsupervised layer-wise pretraining does not exploit information from class labels. Here, we propose a new regularization technique, called diversifying regularization (DR), which applies a penalty on hi…

Diminishing-returns (DR) submodular optimization is an important field with many real-world applications in machine learning, economics and communication systems. It captures a subclass of non-convex optimization that provides both practical and theoretical guarantees. In this paper, we study the fundamental problem of…

Dynamic regressor selection (DRS) systems work by selecting the most competent regressors from an ensemble to estimate the target value of a given test pattern. This competence is usually quantified using the performance of the regressors in local regions of the feature space around the test pattern. However, choosing …

ProbDR framework interprets DR algorithms as probabilistic inference.

DRSS method identifies unnecessary samples and features in DR covariate shift.

Adapts DR objectives for both sample and feature size reduction.

Dimension Estimation (DE) and Dimension Reduction (DR) are two closely related topics, but with quite different goals. In DE, one attempts to estimate the intrinsic dimensionality or number of latent variables in a set of measurements of a random vector. However, in DR, one attempts to project a random vector, either l…

Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional density itself is preferable, but conditional density estimation (CDE) is challeng…

In this paper, we study fundamental problems of maximizing DR-submodular continuous functions that have real-world applications in the domain of machine learning, economics, operations research and communication systems. It captures a subclass of non-convex optimization that provides both theoretical and practical guar…

Many researchers implicitly assume that neural networks learn relations and generalise them to new unseen data. It has been shown recently, however, that the generalisation of feed-forward networks fails for identity relations.The proposed solution for this problem is to create an inductive bias with Differential Recti…

The study defines new surfaces with specific cut locus properties and provides conditions for their existence.

Price responsiveness is a major feature of end use customers (EUCs) that participate in demand response (DR) programs, and has been conventionally modeled with static demand functions, which take the electricity price as the input and the aggregate energy consumption as the output. This, however, neglects the inherent …

In this paper, we investigate Dimensionality reduction (DR) maps in an information retrieval setting from a quantitative topology point of view. In particular, we show that no DR maps can achieve perfect precision and perfect recall simultaneously. Thus a continuous DR map must have imperfect precision. We further prov…

The paper examines soliton surfaces using a parallel transport frame field in 4D space.

Proposes DR-ACI for causal effect intervals with temporal dependence.

New method tackles online DR-submodular maximization with improved regret guarantees.