Related papers: Inequalities for Optimization of Classification Al…

In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…

In this work, we propose a PAC-Bayes bound for the generalization risk of the Gibbs classifier in the multi-class classification framework. The novelty of our work is the critical use of the confusion matrix of a classifier as an error…

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…

A machine learning model is calibrated if its predicted probability for an outcome matches the observed frequency for that outcome conditional on the model prediction. This property has become increasingly important as the impact of machine…

Unsupervised feature selection has been always attracting research attention in the communities of machine learning and data mining for decades. In this paper, we propose an unsupervised feature selection method seeking a feature…

Automated medical image segmentation inherently involves a certain degree of uncertainty. One key factor contributing to this uncertainty is the ambiguity that can arise in determining the boundaries of a target region of interest,…

Transductive few-shot learning has recently triggered wide attention in computer vision. Yet, current methods introduce key hyper-parameters, which control the prediction statistics of the test batches, such as the level of class balance,…

Experimental design is central to science and engineering. A ubiquitous challenge is how to maximize the value of information obtained from expensive or constrained experimental settings. Bayesian optimal experimental design (OED) provides…

Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As…

This paper deals with the quantum optimal discrimination among mixed quantum states enjoying geometrical uniform symmetry with respect to a reference density operator $\rho_0$. It is well-known that the minimal error probability is given by…

The Gershgorin Circle Theorem is a well-known and efficient method for bounding the eigenvalues of a matrix in terms of its entries. If $A$ is a symmetric matrix, by writing $A = B + x{\bf 1}$, where ${\bf 1}$ is the matrix with unit…

An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…

Many classification performance metrics exist, each suited to a specific application. However, these metrics often differ in scale and can exhibit varying sensitivity to class imbalance rates in the test set. As a result, it is difficult to…

Multiclass classification problems such as image annotation can involve a large number of classes. In this context, confusion between classes can occur, and single label classification may be misleading. We provide in the present paper a…

The Area under the ROC curve (AUC) is a well-known ranking metric for problems such as imbalanced learning and recommender systems. The vast majority of existing AUC-optimization-based machine learning methods only focus on binary-class…

Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…

The ultimate performance of machine learning algorithms for classification tasks is usually measured in terms of the empirical error probability (or accuracy) based on a testing dataset. Whereas, these algorithms are optimized through the…

We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…

The interplay between missing data and model uncertainty -- two classic statistical problems -- leads to primary questions that we formally address from an objective Bayesian perspective. For the general regression problem, we discuss the…

Uncertainty in optimization is often represented as stochastic parameters in the optimization model. In Predict-Then-Optimize approaches, predictions of a machine learning model are used as values for such parameters, effectively…