We study the $p$-generalized probit regression model, which is a generalized linear model for binary responses. It extends the standard probit model by replacing its link function, the standard normal cdf, by a $p$-generalized normal distribution for $p\in[1, \infty)$. The $p$-generalized normal distributions \citep{Sub23} are of special interest in statistical modeling because they fit much more flexibly to data. Their tail behavior can be controlled by choice of the parameter $p$, which influences the model's sensitivity to outliers. Special cases include the Laplace, the Gaussian, and the uniform distributions. We further show how the maximum likelihood estimator for $p$-generalized probit regression can be approximated efficiently up to a factor of $(1+\varepsilon)$ on large data by combining sketching techniques with importance subsampling to obtain a small data summary called coreset.

The Dirichlet Process Gaussian Mixture Model (DPGMM) is often used to cluster data when the number of clusters is unknown. One main DPGMM inference paradigm relies on sampling. Here we consider a known state-of-art sampler (proposed by Chang and Fisher III (2013) and improved by Dinari et al. (2019)), analyze its failure modes, and show how to improve it, often drastically. Concretely, in that sampler, whenever a new cluster is formed it is augmented with two subclusters whose labels are initialized at random. Upon their evolution, the subclusters serve to propose a split of the parent cluster. We show that the random initialization is often problematic and hurts the otherwise-effective sampler. Specifically, we demonstrate that this initialization tends to lead to poor split proposals and/or too many iterations before a desired split is accepted. This slows convergence and can damage the clustering. As a remedy, we propose two drop-in-replacement options for the subcluster-initialization subroutine. The first is an intuitive heuristic while the second is based on deep learning. We show that the proposed approach yields better splits, which in turn translate to substantial improvements in performance, results, and stability.

With the rising use of the Internet in today's society, the quantity of data created is incomprehensibly huge. Even though the nature of individual data is straightforward, the sheer amount of data to be analyzed makes processing difficult for even computers. To manage such procedures, we need large data analysis tools. Data mining methods and techniques, in conjunction with machine learning, enable us to analyze large amounts of data in an intelligible manner. It is capable of classifying unlabeled data into a predetermined number of clusters based on similarities (k).

Novel prediction methods should always be compared to a baseline to know how well they perform. Without this frame of reference, the performance score of a model is basically meaningless. What does it mean when a model achieves an $F_1$ of 0.8 on a test set? A proper baseline is needed to evaluate the `goodness' of a performance score. Comparing with the latest state-of-the-art model is usually insightful. However, being state-of-the-art can change rapidly when newer models are developed. Contrary to an advanced model, a simple dummy classifier could be used. However, the latter could be beaten too easily, making the comparison less valuable. This paper presents a universal baseline method for all binary classification models, named the Dutch Draw (DD). This approach weighs simple classifiers and determines the best classifier to use as a baseline. We theoretically derive the DD baseline for many commonly used evaluation measures and show that in most situations it reduces to (almost) always predicting either zero or one. Summarizing, the DD baseline is: (1) general, as it is applicable to all binary classification problems; (2) simple, as it is quickly determined without training or parameter-tuning; (3) informative, as insightful conclusions can be drawn from the results. The DD baseline serves two purposes. First, to enable comparisons across research papers by this robust and universal baseline. Secondly, to provide a sanity check during the development process of a prediction model. It is a major warning sign when a model is outperformed by the DD baseline.

Plastic waste is a significant environmental pollutant that is difficult to monitor. We created a system of neural networks to analyze spectral, spatial, and temporal components of Sentinel-2 satellite data to identify terrestrial aggregations of waste. The system works at continental scale. We evaluated performance in Indonesia and detected 374 waste aggregations, more than double the number of sites found in public databases. The same system deployed across twelve countries in Southeast Asia identifies 996 subsequently confirmed waste sites. For each detected site, we algorithmically monitor waste site footprints through time and cross-reference other datasets to generate physical and social metadata. 19% of detected waste sites are located within 200 m of a waterway. Numerous sites sit directly on riverbanks, with high risk of ocean leakage.

Recently, many researchers have advanced data-driven methods for modeling heterogeneous treatment effects (HTEs). Even still, estimation of HTEs is a difficult task -- these methods frequently over- or under-estimate the treatment effects, leading to poor calibration of the resulting models. However, while many methods exist for evaluating the calibration of prediction and classification models, formal approaches to assess the calibration of HTE models are limited to the calibration slope. In this paper, we define an analogue of the \smash{($\ell_2$)} expected calibration error for HTEs, and propose a robust estimator. Our approach is motivated by doubly robust treatment effect estimators, making it unbiased, and resilient to confounding, overfitting, and high-dimensionality issues. Furthermore, our method is straightforward to adapt to many structures under which treatment effects can be identified, including randomized trials, observational studies, and survival analysis. We illustrate how to use our proposed metric to evaluate the calibration of learned HTE models through the application to the CRITEO-UPLIFT Trial.

We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as Nystr\"om samples. We consider an unweighted variation of the radial squared-kernel discrepancy (SKD) criterion as a surrogate for the classical criteria used to assess the Nystr\"om approximation accuracy; in this setting, we discuss how Nystr\"om samples can be efficiently optimised through stochastic gradient descent. We perform numerical experiments which demonstrate that the local minimisation of the radial SKD yields Nystr\"om samples with improved Nystr\"om approximation accuracy.

The right to be forgotten has been legislated in many countries, but its enforcement in the AI industry would cause unbearable costs. When single data deletion requests come, companies may need to delete the whole models learned with massive resources. Existing works propose methods to remove knowledge learned from data for explicitly parameterized models, which however are not appliable to the sampling-based Bayesian inference, i.e., Markov chain Monte Carlo (MCMC), as MCMC can only infer implicit distributions. In this paper, we propose the first machine unlearning algorithm for MCMC. We first convert the MCMC unlearning problem into an explicit optimization problem. Based on this problem conversion, an MCMC influence function is designed to provably characterize the learned knowledge from data, which then delivers the MCMC unlearning algorithm. Theoretical analysis shows that MCMC unlearning would not compromise the generalizability of the MCMC models. Experiments on Gaussian mixture models and Bayesian neural networks confirm the effectiveness of the proposed algorithm. "The right to be forgotten" refers to the right of individuals to request data controllers such as tech giants to delete the data collected from them. It has been recognized in many countries through legislation, including the European Union's General Data Protection Regulation (2016) and the California Consumer Privacy Act (2018).

Transformers trained with self-supervised learning using self-distillation loss (DINO) have been shown to produce attention maps that highlight salient foreground objects. In this paper, we demonstrate a graph-based approach that uses the self-supervised transformer features to discover an object from an image. Visual tokens are viewed as nodes in a weighted graph with edges representing a connectivity score based on the similarity of tokens. Foreground objects can then be segmented using a normalized graph-cut to group self-similar regions. We solve the graph-cut problem using spectral clustering with generalized eigen-decomposition and show that the second smallest eigenvector provides a cutting solution since its absolute value indicates the likelihood that a token belongs to a foreground object. Despite its simplicity, this approach significantly boosts the performance of unsupervised object discovery: we improve over the recent state of the art LOST by a margin of 6.9%, 8.1%, and 8.1% respectively on the VOC07, VOC12, and COCO20K. The performance can be further improved by adding a second stage class-agnostic detector (CAD). Our proposed method can be easily extended to unsupervised saliency detection and weakly supervised object detection. For unsupervised saliency detection, we improve IoU for 4.9%, 5.2%, 12.9% on ECSSD, DUTS, DUT-OMRON respectively compared to previous state of the art. For weakly supervised object detection, we achieve competitive performance on CUB and ImageNet.

When trained on diverse labeled data, machine learning models have proven themselves to be a powerful tool in all facets of society. However, due to budget limitations, deliberate or non-deliberate censorship, and other problems during data collection and curation, the labeled training set might exhibit a systematic shortage of data for certain groups. We investigate a scenario in which the absence of certain data is linked to the second level of a two-level hierarchy in the data. Inspired by the idea of protected groups from algorithmic fairness, we refer to the partitions carved by this second level as "subgroups"; we refer to combinations of subgroups and classes, or leaves of the hierarchy, as "sources". To characterize the problem, we introduce the concept of classes with incomplete subgroup support. The representational bias in the training set can give rise to spurious correlations between the classes and the subgroups which render standard classification models ungeneralizable to unseen sources. To overcome this bias, we make use of an additional, diverse but unlabeled dataset, called the "deployment set", to learn a representation that is invariant to subgroup. This is done by adversarially matching the support of the training and deployment sets in representation space. In order to learn the desired invariance, it is paramount that the sets of samples observed by the discriminator are balanced by class; this is easily achieved for the training set, but requires using semi-supervised clustering for the deployment set. We demonstrate the effectiveness of our method with experiments on several datasets and variants of the problem.