arXiv research

We study consistency of learning algorithms for a multi-class performance metric that is a non-decomposable function of the confusion matrix of a classifier and cannot be expressed as a sum of losses on individual data points; examples of such performance metrics include the macro F-measure popular in information retri…

A new method for optimizing non-decomposable metrics with constraints.

Paper tackles noisy labels for non-decomposable performance measures.

DeepTopPush improves accuracy at the top for complex classification tasks.

SelMix fine-tunes pre-trained models to optimize non-decomposable objectives.

Develops a new minimax probability machine for imbalanced classification tasks.

We provide a general theoretical analysis of expected out-of-sample utility, also referred to as decision-theoretic classification, for non-decomposable binary classification metrics such as F-measure and Jaccard coefficient. Our key result is that the expected out-of-sample utility for many performance metrics is prov…

Modern applications in sensitive domains such as biometrics and medicine frequently require the use of non-decomposable loss functions such as precision@k, F-measure etc. Compared to point loss functions such as hinge-loss, these offer much more fine grained control over prediction, but at the same time present novel c…

A new method, VIF, calculates influence for non-decomposable losses efficiently.

Vision problems ranging from image clustering to motion segmentation to semi-supervised learning can naturally be framed as subspace segmentation problems, in which one aims to recover multiple low-dimensional subspaces from noisy and corrupted input data. Low-Rank Representation (LRR), a convex formulation of the subs…

New framework for optimizing machine learning risks.

Stochastic Gradient Descent has been widely studied with classification accuracy as a performance measure. However, these stochastic algorithms cannot be directly used when non-decomposable pairwise performance measures are used such as Area under the ROC curve (AUC) which is a common performance metric when the classe…

We consider the problem of recommending relevant labels (items) for a given data point (user). In particular, we are interested in the practically important setting where the evaluation is with respect to non-decomposable (over labels) performance metrics like the $F_1$ measure, and the training data has missing labels…

We present a class of algorithms capable of directly training deep neural networks with respect to large families of task-specific performance measures such as the F-measure and the Kullback-Leibler divergence that are structured and non-decomposable. This presents a departure from standard deep learning techniques tha…

We propose a method that enables practitioners to conveniently incorporate custom non-decomposable performance metrics into differentiable learning pipelines, notably those based upon neural network architectures. Our approach is based on the recently developed adversarial prediction framework, a distributionally robus…

Modern classification problems frequently present mild to severe label imbalance as well as specific requirements on classification characteristics, and require optimizing performance measures that are non-decomposable over the dataset, such as F-measure. Such measures have spurred much interest and pose specific chall…

Unified approach for fair classification with overlapping groups.

We introduce backdrop, a flexible and simple-to-implement method, intuitively described as dropout acting only along the backpropagation pipeline. Backdrop is implemented via one or more masking layers which are inserted at specific points along the network. Each backdrop masking layer acts as the identity in the forwa…

Generating adversarial examples is a critical step for evaluating and improving the robustness of learning machines. So far, most existing methods only work for classification and are not designed to alter the true performance measure of the problem at hand. We introduce a novel flexible approach named Houdini for gene…

We investigate the ramifications of the Legendrian satellite construction on the relation of Lagrangian cobordism between Legendrian knots. Under a simple hypothesis, we construct a Lagrangian concordance between two Legendrian satellites by stacking up a sequence of elementary cobordisms. This construction narrows the…

We present a general framework for solving a large class of learning problems with non-linear functions of classification rates. This includes problems where one wishes to optimize a non-decomposable performance metric such as the F-measure or G-mean, and constrained training problems where the classifier needs to sati…

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cas…

The study connects fairness constraints with optimal transport to derive new insights in classification.

We propose a framework for constructing and analyzing multiclass and multioutput classification metrics, i.e., involving multiple, possibly correlated multiclass labels. Our analysis reveals novel insights on the geometry of feasible confusion tensors -- including necessary and sufficient conditions for the equivalence…

Using gauge theory for Spin(7)-manifolds of dimension 8, we develop a procedure, called Spin-rotation, which transforms a (stable) holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new holomorphic structure over a different complex torus. We show non-trivial examples of this procedure …

New method reduces bias and variance in OPE for large action spaces.

In classification models fairness can be ensured by solving a constrained optimization problem. We focus on fairness constraints like Disparate Impact, Demographic Parity, and Equalized Odds, which are non-decomposable and non-convex. Researchers define convex surrogates of the constraints and then apply convex optimiz…

The minimization of loss functions is the heart and soul of Machine Learning. In this paper, we propose an off-the-shelf optimization approach that can minimize virtually any non-differentiable and non-decomposable loss function (e.g. Miss-classification Rate, AUC, F1, Jaccard Index, Mathew Correlation Coefficient, etc…

We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…

New algorithm optimizes complex metrics in online learning.

Develops gradient boosting for multi-label classification.

Modern retrieval systems are often driven by an underlying machine learning model. The goal of such systems is to identify and possibly rank the few most relevant items for a given query or context. Thus, such systems are typically evaluated using a ranking-based performance metric such as the area under the precision-…

Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics remains a challenge due to their non-differentiable and non-decomposable nature. We present an efficient, theoretically sound, and general met…

Range penalization enhances statistical accuracy and resource efficiency in federated learning.

We prove that for any open Riemann surface $N,$ natural number $n\geq 3,$ non-constant harmonic map $h:N\to \mathbb{R}^{n-2}$ and holomorphic 2-form $H$ on $N,$ there exists a weakly complete harmonic map $X=(X_j)_{j=1,\ldots,n}:N \to \mathbb{R}^n$ with Hopf differential $H$ and $(X_j)_{j=3,\ldots,n}=h.$ In particular,…

We propose a Bayesian approximate inference method for learning the dependence structure of a Gaussian graphical model. Using pseudo-likelihood, we derive an analytical expression to approximate the marginal likelihood for an arbitrary graph structure without invoking any assumptions about decomposability. The majority…

This paper tackles unbiased loss functions for multilabel classification with missing labels.

Introduces robust and decomposable AP for image retrieval.

Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decom…

This paper explores methods for combining predictions in multilabel classification.

Improved FDAM algorithms for heterogeneous data with constant communication complexity.

We present a framework and analysis of consistent binary classification for complex and non-decomposable performance metrics such as the F-measure and the Jaccard measure. The proposed framework is general, as it applies to both batch and online learning, and to both linear and non-linear models. Our work follows recen…

FeDXL tackles federated learning for X-risk optimization.

Bayesian learning for forests and trees improves graph detection and structure learning.

Improved performance of factorized neural layers through spectral initialization and Frobenius decay.

The paper explores when and why value decomposition algorithms work in cooperative multi-agent reinforcement learning.

We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…

Optimal transport reformulates multiple quantile hedging problem.