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Clustering is an important task in many areas of knowledge: medicine and epidemiology, genomics, environmental science, economics, visual sciences, among others. Methodologies to perform inference on the number of clusters have often been proved to be inconsistent, and introducing a dependence structure among the clusters implies additional difficulties in the estimation process. In a Bayesian setting, clustering is performed by considering the unknown partition as a random object and define a prior distribution on it. This prior distribution may be induced by models on the observations, or directly defined for the partition. Several recent results, however, have shown the difficulties in consistently estimating the number of clusters, and, therefore, the partition. The problem itself of summarising the posterior distribution on the partition remains open, given the large dimension of the partition space. This work aims at reviewing the Bayesian approaches available in the literature to perform clustering, presenting advantages and disadvantages of each of them in order to suggest future lines of research.

The popularity of point cloud deep models for safety-critical purposes has increased, but the reliability and security of these models can be compromised by intentional or naturally occurring point cloud noise. To combat this issue, we present a novel point cloud outlier removal method called PointCVaR, which empowers standard-trained models to eliminate additional outliers and restore the data. Our approach begins by conducting attribution analysis to determine the influence of each point on the model output, which we refer to as point risk. We then optimize the process of filtering high-risk points using Conditional Value at Risk (CVaR) as the objective. The rationale for this approach is based on the observation that noise points in point clouds tend to cluster in the tail of the risk distribution, with a low frequency but a high level of risk, resulting in significant interference with classification results. Despite requiring no additional training effort, our method produces exceptional results in various removal-and-classification experiments for noisy point clouds, which are corrupted by random noise, adversarial noise, and backdoor trigger noise. Impressively, it achieves 87% accuracy in defense against the backdoor attack by removing triggers. Overall, the proposed PointCVaR effectively eliminates noise points and enhances point cloud classification, making it a promising plug-in module for various models in different scenarios.

This paper focuses on the substantive application of multilevel LCA to the evolution of citizenship norms in a diverse array of democratic countries. To do so, we present a two-stage approach to fit multilevel latent class models: in the first stage (measurement model construction), unconditional class enumeration is done separately on both low and high level latent variables, estimating only a part of the model at a time -- hence keeping the remaining part fixed -- and then updating the full measurement model; in the second stage (structural model construction), individual and/or group covariates are included in the model. By separating the two parts -- first stage and second stage of model building -- the measurement model is stabilized and is allowed to be determined only by it's indicators. Moreover, this two-step approach makes the inclusion/exclusion of a covariate a relatively simple task to handle. Our proposal amends common practice in applied social science research, where simple (low-level) LCA is done to obtain a classification of low-level unit, and this is then related to (low- and high-level) covariates simply including group fixed effects. Our analysis identifies latent classes that score either consistently high or consistently low on all measured items, along with two theoretically important classes that place distinctive emphasis on items related to engaged citizenship, and duty-based norms.

We consider the problem of model selection when grouping structure is inherent within the regressors. Using a Bayesian approach, we model the mean vector by a one-group global-local shrinkage prior belonging to a broad class of such priors that includes the horseshoe prior. In the context of variable selection, this class of priors was studied by Tang et al. (2018) \cite{tang2018bayesian}. A modified form of the usual class of global-local shrinkage priors with polynomial tail on the group regression coefficients is proposed. The resulting threshold rule selects the active group if within a group, the ratio of the $L_2$ norm of the posterior mean of its group coefficient to that of the corresponding ordinary least square group estimate is greater than a half. In the theoretical part of this article, we have used the global shrinkage parameter either as a tuning one or an empirical Bayes estimate of it depending on the knowledge regarding the underlying sparsity of the model. When the proportion of active groups is known, using $\tau$ as a tuning parameter, we have proved that our method enjoys variable selection consistency. In case this proportion is unknown, we propose an empirical Bayes estimate of $\tau$. Even if this empirical Bayes estimate is used, then also our half-thresholding rule captures the true sparse group structure. Though our theoretical works rely on a special form of the design matrix, but for general design matrices also, our simulation results show that the half-thresholding rule yields results similar to that of Yang and Narisetty (2020) \cite{yang2020consistent}. As a consequence of this, in a high dimensional sparse group selection problem, instead of using the so-called `gold standard' spike and slab prior, one can use the one-group global-local shrinkage priors with polynomial tail to obtain similar results.

We consider the problem of learning from data corrupted by underrepresentation bias, where positive examples are filtered from the data at different, unknown rates for a fixed number of sensitive groups. We show that with a small amount of unbiased data, we can efficiently estimate the group-wise drop-out parameters, even in settings where intersectional group membership makes learning each intersectional rate computationally infeasible. Using this estimate for the group-wise drop-out rate, we construct a re-weighting scheme that allows us to approximate the loss of any hypothesis on the true distribution, even if we only observe the empirical error on a biased sample. Finally, we present an algorithm encapsulating this learning and re-weighting process, and we provide strong PAC-style guarantees that, with high probability, our estimate of the risk of the hypothesis over the true distribution will be arbitrarily close to the true risk.

We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data, while maintaining type I error control. We build upon the principle of (nonparametric) testing by betting, where a gambler places bets on future observations and their wealth measures evidence against the null hypothesis. While recently developed kernel-based betting strategies often work well on simple distributions, selecting a suitable kernel for high-dimensional or structured data, such as images, is often nontrivial. To address this drawback, we design prediction-based betting strategies that rely on the following fact: if a sequentially updated predictor starts to consistently determine (a) which distribution an instance is drawn from, or (b) whether an instance is drawn from the joint distribution or the product of the marginal distributions (the latter produced by external randomization), it provides evidence against the two-sample or independence nulls respectively. We empirically demonstrate the superiority of our tests over kernel-based approaches under structured settings. Our tests can be applied beyond the case of independent and identically distributed data, remaining valid and powerful even when the data distribution drifts over time.

Learning on big data brings success for artificial intelligence (AI), but the annotation and training costs are expensive. In future, learning on small data is one of the ultimate purposes of AI, which requires machines to recognize objectives and scenarios relying on small data as humans. A series of machine learning models is going on this way such as active learning, few-shot learning, deep clustering. However, there are few theoretical guarantees for their generalization performance. Moreover, most of their settings are passive, that is, the label distribution is explicitly controlled by one specified sampling scenario. This survey follows the agnostic active sampling under a PAC (Probably Approximately Correct) framework to analyze the generalization error and label complexity of learning on small data using a supervised and unsupervised fashion. With these theoretical analyses, we categorize the small data learning models from two geometric perspectives: the Euclidean and non-Euclidean (hyperbolic) mean representation, where their optimization solutions are also presented and discussed. Later, some potential learning scenarios that may benefit from small data learning are then summarized, and their potential learning scenarios are also analyzed. Finally, some challenging applications such as computer vision, natural language processing that may benefit from learning on small data are also surveyed.

Data augmentation, the artificial creation of training data for machine learning by transformations, is a widely studied research field across machine learning disciplines. While it is useful for increasing the generalization capabilities of a model, it can also address many other challenges and problems, from overcoming a limited amount of training data over regularizing the objective to limiting the amount data used to protect privacy. Based on a precise description of the goals and applications of data augmentation (C1) and a taxonomy for existing works (C2), this survey is concerned with data augmentation methods for textual classification and aims to achieve a concise and comprehensive overview for researchers and practitioners (C3). Derived from the taxonomy, we divided more than 100 methods into 12 different groupings and provide state-of-the-art references expounding which methods are highly promising (C4). Finally, research perspectives that may constitute a building block for future work are given (C5).

In recent years, there has been an exponential growth in the number of complex documents and texts that require a deeper understanding of machine learning methods to be able to accurately classify texts in many applications. Many machine learning approaches have achieved surpassing results in natural language processing. The success of these learning algorithms relies on their capacity to understand complex models and non-linear relationships within data. However, finding suitable structures, architectures, and techniques for text classification is a challenge for researchers. In this paper, a brief overview of text classification algorithms is discussed. This overview covers different text feature extractions, dimensionality reduction methods, existing algorithms and techniques, and evaluations methods. Finally, the limitations of each technique and their application in the real-world problem are discussed.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.