Knowing what you know: valid and validated631 confidence sets in multiclass and multilabel prediction.

Surfacing the hidden beauty of flickr pictures.

Given samples from an unknown discrete distribution p, is it possible to distinguish whether p belongs to some class of distributions C versus p being far from every distribution in C? This fundamental question has received tremendous attention in statistics, focusing primarily on asymptotic analysis, as well as in information theory and theoretical computer science, where the emphasis has been on small sample size and computational complexity. Nevertheless, even for basic properties of discrete distributions such as monotonicity, independence, log-concavity, unimodality, and monotone-hazard rate, the optimal sample complexity is unknown. We provide a general approach via which we obtain sample-optimal and computationally efficient testers for all these distribution families.

Ordinal regression (OR, also called ordinal classification) is classification of ordinal data, in which the underlying target variable is categorical and considered to have a natural ordinal relation for the underlying explanatory variable. A key to successful OR models is to find a data structure `natural ordinal relation' common to many ordinal data and reflect that structure into the design of those models. A recent OR study found that many real-world ordinal data show a tendency that the conditional probability distribution (CPD) of the target variable given a value of the explanatory variable will often be unimodal. Several previous studies thus developed unimodal likelihood models, in which a predicted CPD is guaranteed to become unimodal. However, it was also observed experimentally that many real-world ordinal data partly have values of the explanatory variable where the underlying CPD will be non-unimodal, and hence unimodal likelihood models may suffer from a bias for such a CPD. Therefore, motivated to mitigate such a bias, we propose approximately unimodal likelihood models, which can represent up to a unimodal CPD and a CPD that is close to be unimodal. We also verify experimentally that a proposed model can be effective for statistical modeling of ordinal data and OR tasks.

Multimodal Emotion Recognition (MER) often encounters incomplete multimodality in practical applications due to sensor failures or privacy protection requirements. While existing methods attempt to address various incomplete multimodal scenarios by balancing the training of each modality combination through additional gradients, these approaches face a critical limitation: training gradients from different modality combinations conflict with each other, ultimately degrading the performance of the final prediction model. In this paper, we propose a unimodal decoupled dynamic low-rank adaptation method based on modality combinations, named MCULoRA, which is a novel framework for the parameter-efficient training of incomplete multimodal learning models. MCULoRA consists of two key modules, modality combination aware low-rank adaptation (MCLA) and dynamic parameter fine-tuning (DPFT). The MCLA module effectively decouples the shared information from the distinct characteristics of individual modality combinations. The DPFT module adjusts the training ratio of modality combinations based on the separability of each modality's representation space, optimizing the learning efficiency across different modality combinations. Our extensive experimental evaluation in multiple benchmark datasets demonstrates that MCULoRA substantially outperforms previous incomplete multimodal learning approaches in downstream task accuracy.

Unimodality constitutes a key property indicating grouping behavior of the data around a single mode of its density. We propose a method that partitions univariate data into unimodal subsets through recursive splitting around valley points of the data density. For valley point detection, we introduce properties of critical points on the convex hull of the empirical cumulative density function (ecdf) plot that provide indications on the existence of density valleys. Next, we apply a unimodal data modeling approach that provides a statistical model for each obtained unimodal subset in the form of a Uniform Mixture Model (UMM). Consequently, a hierarchical statistical model of the initial dataset is obtained in the form of a mixture of UMMs, named as the Unimodal Mixture Model (UDMM). The proposed method is non-parametric, hyperparameter-free, automatically estimates the number of unimodal subsets and provides accurate statistical models as indicated by experimental results on clustering and density estimation tasks.

Recent studies have shown that deep neural networks are not well-calibrated and often produce over-confident predictions. The miscalibration issue primarily stems from using cross-entropy in classifications, which aims to align predicted softmax probabilities with one-hot labels. In ordinal regression tasks, this problem is compounded by an additional challenge: the expectation that softmax probabilities should exhibit unimodal distribution is not met with cross-entropy. The ordinal regression literature has focused on learning orders and overlooked calibration. To address both issues, we propose a novel loss function that introduces order-aware calibration, ensuring that prediction confidence adheres to ordinal relationships between classes. It incorporates soft ordinal encoding and order-aware regularization to enforce both calibration and unimodality. Extensive experiments across three popular ordinal regression benchmarks demonstrate that our approach achieves state-of-the-art calibration without compromising accuracy.

Learning the number of clusters is a key problem in data clustering. We present dip-means, a novel robust incremental method to learn the number of data clusters that can be used as a wrapper around any iterative clustering algorithm of k-means family. In contrast to many popular methods which make assumptions about the underlying cluster distributions, dip-means only assumes a fundamental cluster property: each cluster to admit a unimodal distribution. The proposed algorithm considers each cluster member as an individual'viewer' and applies a univariate statistic hypothesis test for unimodality (dip-test) on the distribution of distances between the viewer and the cluster members. Important advantages are: i) the unimodality test is applied on univariate distance vectors, ii) it can be directly applied with kernel-based methods, since only the pairwise distances are involved in the computations. Experimental results on artificial and real datasets indicate the effectiveness of our method and its superiority over analogous approaches.