Two-sample testing tests whether the distributions generating two samples are identical. We pose the two-sample testing problem in a new scenario where the sample measurements (or sample features) are inexpensive to access, but their group memberships (or labels) are costly. We devise the first \emph{active sequential two-sample testing framework} that not only sequentially but also \emph{actively queries} sample labels to address the problem. Our test statistic is a likelihood ratio where one likelihood is found by maximization over all class priors, and the other is given by a classification model. The classification model is adaptively updated and then used to guide an active query scheme called bimodal query to label sample features in the regions with high dependency between the feature variables and the label variables. The theoretical contributions in the paper include proof that our framework produces an \emph{anytime-valid} $p$-value; and, under reachable conditions and a mild assumption, the framework asymptotically generates a minimum normalized log-likelihood ratio statistic that a passive query scheme can only achieve when the feature variable and the label variable have the highest dependence. Lastly, we provide a \emph{query-switching (QS)} algorithm to decide when to switch from passive query to active query and adapt bimodal query to increase the testing power of our test. Extensive experiments justify our theoretical contributions and the effectiveness of QS.

The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in important applications ranging from kernel methods to efficient Transformers. We propose parameterized, positive, non-trigonometric RFs which approximate Gaussian and softmax-kernels. In contrast to traditional RF approximations, parameters of these new methods can be optimized to reduce the variance of the approximation, and the optimum can be expressed in closed form. We show that our methods lead to variance reduction in practice ($e^{10}$-times smaller variance and beyond) and outperform previous methods in a kernel regression task. Using our proposed mechanism, we also present FAVOR#, a method for self-attention approximation in Transformers. We show that FAVOR# outperforms other random feature methods in speech modelling and natural language processing.

Stochastic gradient descent plays a fundamental role in nearly all applications of deep learning. However its ability to converge to a global minimum remains shrouded in mystery. In this paper we propose to study the behavior of the loss function on fixed mini-batches along SGD trajectories. We show that the loss function on a fixed batch appears to be remarkably convex-like. In particular for ResNet the loss for any fixed mini-batch can be accurately modeled by a quadratic function and a very low loss value can be reached in just one step of gradient descent with sufficiently large learning rate. We propose a simple model that allows to analyze the relationship between the gradients of stochastic mini-batches and the full batch. Our analysis allows us to discover the equivalency between iterate aggregates and specific learning rate schedules. In particular, for Exponential Moving Average (EMA) and Stochastic Weight Averaging we show that our proposed model matches the observed training trajectories on ImageNet. Our theoretical model predicts that an even simpler averaging technique, averaging just two points a many steps apart, significantly improves accuracy compared to the baseline. We validated our findings on ImageNet and other datasets using ResNet architecture.

It is well known that the finite step-size ($h$) in Gradient Descent (GD) implicitly regularizes solutions to flatter minima. A natural question to ask is "Does the momentum parameter $\beta$ play a role in implicit regularization in Heavy-ball (H.B) momentum accelerated gradient descent (GD+M)?". To answer this question, first, we show that the discrete H.B momentum update (GD+M) follows a continuous trajectory induced by a modified loss, which consists of an original loss and an implicit regularizer. Then, we show that this implicit regularizer for (GD+M) is stronger than that of (GD) by factor of $(\frac{1+\beta}{1-\beta})$, thus explaining why (GD+M) shows better generalization performance and higher test accuracy than (GD). Furthermore, we extend our analysis to the stochastic version of gradient descent with momentum (SGD+M) and characterize the continuous trajectory of the update of (SGD+M) in a pointwise sense. We explore the implicit regularization in (SGD+M) and (GD+M) through a series of experiments validating our theory.

A time series is a sequence of sequentially ordered real values in time. Time series classification (TSC) is the task of assigning a time series to one of a set of predefined classes, usually based on a model learned from examples. Dictionary-based methods for TSC rely on counting the frequency of certain patterns in time series and are important components of the currently most accurate TSC ensembles. One of the early dictionary-based methods was WEASEL, which at its time achieved SotA results while also being very fast. However, it is outperformed both in terms of speed and accuracy by other methods. Furthermore, its design leads to an unpredictably large memory footprint, making it inapplicable for many applications. In this paper, we present WEASEL 2.0, a complete overhaul of WEASEL based on two recent advancements in TSC: Dilation and ensembling of randomized hyper-parameter settings. These two techniques allow WEASEL 2.0 to work with a fixed-size memory footprint while at the same time improving accuracy. Compared to 15 other SotA methods on the UCR benchmark set, WEASEL 2.0 is significantly more accurate than other dictionary methods and not significantly worse than the currently best methods. Actually, it achieves the highest median accuracy over all data sets, and it performs best in 5 out of 12 problem classes. We thus believe that WEASEL 2.0 is a viable alternative for current TSC and also a potentially interesting input for future ensembles.

Besides far-reaching public health consequences, the COVID-19 pandemic had a significant psychological impact on people around the world. To gain further insight into this matter, we introduce the Real World Worry Waves Dataset (RW3D). The dataset combines rich open-ended free-text responses with survey data on emotions, significant life events, and psychological stressors in a repeated-measures design in the UK over three years (2020: n = 2441, 2021: n = 1716 and 2022: n = 1152). This paper provides background information on the data collection procedure, the recorded variables, participants' demographics, and higher-order psychological and text-based derived variables that emerged from the data. The RW3D is a unique primary data resource that could inspire new research questions on the psychological impact of the pandemic, especially those that connect modalities (here: text data, psychological survey variables and demographics) over time.

Recent semi-supervised learning algorithms have demonstrated greater success with higher overall performance due to better-unlabeled data representations. Nonetheless, recent research suggests that the performance of the SSL algorithm can be degraded when the unlabeled set contains out-of-distribution examples (OODs). This work addresses the following question: How do out-of-distribution (OOD) data adversely affect semi-supervised learning algorithms? To answer this question, we investigate the critical causes of OOD's negative effect on SSL algorithms. In particular, we found that 1) certain kinds of OOD data instances that are close to the decision boundary have a more significant impact on performance than those that are further away, and 2) Batch Normalization (BN), a popular module, may degrade rather than improve performance when the unlabeled set contains OODs. In this context, we developed a unified weighted robust SSL framework that can be easily extended to many existing SSL algorithms and improve their robustness against OODs. More specifically, we developed an efficient bi-level optimization algorithm that could accommodate high-order approximations of the objective and scale to multiple inner optimization steps to learn a massive number of weight parameters while outperforming existing low-order approximations of bi-level optimization. Further, we conduct a theoretical study of the impact of faraway OODs in the BN step and propose a weighted batch normalization (WBN) procedure for improved performance. Finally, we discuss the connection between our approach and low-order approximation techniques. Our experiments on synthetic and real-world datasets demonstrate that our proposed approach significantly enhances the robustness of four representative SSL algorithms against OODs compared to four state-of-the-art robust SSL strategies.

In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations can often be computationally expensive, and an emulator can be trained to efficiently predict the desired response surface. A widely-used emulator is the Gaussian process (GP), which provides a flexible framework for efficient prediction and uncertainty quantification. Standard GPs, however, do not capture structured sparsity on the underlying response surface, which is present in many applications, particularly in the physical sciences. We thus propose a new hierarchical shrinkage GP (HierGP), which incorporates such structure via cumulative shrinkage priors within a GP framework. We show that the HierGP implicitly embeds the well-known principles of effect sparsity, heredity and hierarchy for analysis of experiments, which allows our model to identify structured sparse features from the response surface with limited data. We propose efficient posterior sampling algorithms for model training and prediction, and prove desirable consistency properties for the HierGP. Finally, we demonstrate the improved performance of HierGP over existing models, in a suite of numerical experiments and an application to dynamical system recovery.

This study investigates the use of Visually Grounded Speech (VGS) models for keyword localisation in speech. The study focusses on two main research questions: (1) Is keyword localisation possible with VGS models and (2) Can keyword localisation be done cross-lingually in a real low-resource setting? Four methods for localisation are proposed and evaluated on an English dataset, with the best-performing method achieving an accuracy of 57%. A new dataset containing spoken captions in Yoruba language is also collected and released for cross-lingual keyword localisation. The cross-lingual model obtains a precision of 16% in actual keyword localisation and this performance can be improved by initialising from a model pretrained on English data. The study presents a detailed analysis of the model's success and failure modes and highlights the challenges of using VGS models for keyword localisation in low-resource settings.

In consumer theory, ranking available objects by means of preference relations yields the most common description of individual choices. However, preference-based models assume that individuals: (1) give their preferences only between pairs of objects; (2) are always able to pick the best preferred object. In many situations, they may be instead choosing out of a set with more than two elements and, because of lack of information and/or incomparability (objects with contradictory characteristics), they may not able to select a single most preferred object. To address these situations, we need a choice-model which allows an individual to express a set-valued choice. Choice functions provide such a mathematical framework. We propose a Gaussian Process model to learn choice functions from choice-data. The proposed model assumes a multiple utility representation of a choice function based on the concept of Pareto rationalization, and derives a strategy to learn both the number and the values of these latent multiple utilities. Simulation experiments demonstrate that the proposed model outperforms the state-of-the-art methods.