Related papers: A Model-Agnostic Algorithm for Bayes Error Determi…

There is a fundamental limitation in the prediction performance that a machine learning model can achieve due to the inevitable uncertainty of the prediction target. In classification problems, this can be characterized by the Bayes error,…

Accurate estimation of Intrinsic Dimensionality (ID) is of crucial importance in many data mining and machine learning tasks, including dimensionality reduction, outlier detection, similarity search and subspace clustering. However, since…

While the performance of machine learning systems has experienced significant improvement in recent years, relatively little attention has been paid to the fundamental question: to what extent can we improve our models? This paper provides…

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise…

Approximate probabilistic inference algorithms are central to many fields. Examples include sequential Monte Carlo inference in robotics, variational inference in machine learning, and Markov chain Monte Carlo inference in statistics. A key…

This work invokes the notion of $f$-divergence to introduce a novel upper bound on the Bayes error rate of a general classification task. We show that the proposed bound can be computed by sampling from the output of a parameterized model.…

In critical decision support systems based on medical imaging, the reliability of AI-assisted decision-making is as relevant as predictive accuracy. Although deep learning models have demonstrated significant accuracy, they frequently…

The paper proposes a novel upper confidence bound (UCB) procedure for identifying the arm with the largest mean in a multi-armed bandit game in the fixed confidence setting using a small number of total samples. The procedure cannot be…

In a Gaussian graphical model, the conditional independence between two variables are characterized by the corresponding zero entries in the inverse covariance matrix. Maximum likelihood method using the smoothly clipped absolute deviation…

Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of…

In statistical classification and machine learning, classification error is an important performance measure, which is minimized by the Bayes decision rule. In practice, the unknown true distribution is usually replaced with a model…

While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…

Machine learning classification systems are susceptible to poor performance when trained with incorrect ground truth labels, even when data is well-curated by expert annotators. As machine learning becomes more widespread, it is…

We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the…

Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…

Unsupervised intrinsic image decomposition (IID) is the process of separating a natural image into albedo and shade without these ground truths. A recent model employing light detection and ranging (LiDAR) intensity demonstrated impressive…

In today's data-driven world, the proliferation of publicly available information raises security concerns due to the information leakage (IL) problem. IL involves unintentionally exposing sensitive information to unauthorized parties via…

Unmeasured covariates constitute one of the important problems in causal inference. Even if there are some unmeasured covariates, some instrumental variable methods such as a two-stage residual inclusion (2SRI) estimator, or a…

AI systems can create, propagate, support, and automate bias in decision-making processes. To mitigate biased decisions, we both need to understand the origin of the bias and define what it means for an algorithm to make fair decisions.…