A hierarchical Bayesian framework is introduced for developing rich mixture models for real-valued time series, partly motivated by important applications in financial time series analysis. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. These observable states are described as a discrete context-tree model. At the bottom level, a different, arbitrary model for real-valued time series -- a base model -- is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Efficient algorithms are introduced that allow for effective, exact Bayesian inference and learning in this setting; in particular, the maximum a posteriori probability (MAP) context-tree model can be identified. These algorithms can be updated sequentially, facilitating efficient online forecasting. The utility of the general framework is illustrated in two particular instances: When autoregressive (AR) models are used as base models, resulting in a nonlinear AR mixture model, and when conditional heteroscedastic (ARCH) models are used, resulting in a mixture model that offers a powerful and systematic way of modelling the well-known volatility asymmetries in financial data. In forecasting, the BCT-X methods are found to outperform state-of-the-art techniques on simulated and real-world data, both in terms of accuracy and computational requirements. In modelling, the BCT-X structure finds natural structure present in the data. In particular, the BCT-ARCH model reveals a novel, important feature of stock market index data, in the form of an enhanced leverage effect.

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.

StepMix is an open-source Python package for the pseudo-likelihood estimation (one-, two- and three-step approaches) of generalized finite mixture models (latent profile and latent class analysis) with external variables (covariates and distal outcomes). In many applications in social sciences, the main objective is not only to cluster individuals into latent classes, but also to use these classes to develop more complex statistical models. These models generally divide into a measurement model that relates the latent classes to observed indicators, and a structural model that relates covariates and outcome variables to the latent classes. The measurement and structural models can be estimated jointly using the so-called one-step approach or sequentially using stepwise methods, which present significant advantages for practitioners regarding the interpretability of the estimated latent classes. In addition to the one-step approach, StepMix implements the most important stepwise estimation methods from the literature, including the bias-adjusted three-step methods with Bolk-Croon-Hagenaars and maximum likelihood corrections and the more recent two-step approach. These pseudo-likelihood estimators are presented in this paper under a unified framework as specific expectation-maximization subroutines. To facilitate and promote their adoption among the data science community, StepMix follows the object-oriented design of the scikit-learn library and provides an additional R wrapper.

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases.

Detecting change-points in data is challenging because of the range of possible types of change and types of behaviour of data when there is no change. Statistically efficient methods for detecting a change will depend on both of these features, and it can be difficult for a practitioner to develop an appropriate detection method for their application of interest. We show how to automatically generate new offline detection methods based on training a neural network. Our approach is motivated by many existing tests for the presence of a change-point being representable by a simple neural network, and thus a neural network trained with sufficient data should have performance at least as good as these methods. We present theory that quantifies the error rate for such an approach, and how it depends on the amount of training data. Empirical results show that, even with limited training data, its performance is competitive with the standard CUSUM-based classifier for detecting a change in mean when the noise is independent and Gaussian, and can substantially outperform it in the presence of auto-correlated or heavy-tailed noise. Our method also shows strong results in detecting and localising changes in activity based on accelerometer data.

While hyperparameter tuning shows theoretical promise, its practical efficacy is not universally superior, as evidenced in Figure 4. The results thus offer a balanced perspective that marries theoretical rigor with empirical validation, fulfilling both academic and practical requirements. Implications for the Field of Machine Learning and Predictive Modeling Robustness and Generalization: The ensemble and stacking methods offer a mathematically substantiated pathway to improve the generalization capabilities of predictive models. Interpretability: The feature integration techniques not only improve model performance but also offer better interpretability by highlighting important features through mathematical formulations. Optimization: The proven convergence of Bayesian Optimization to the global optimum has far-reaching implications for hyperparameter tuning in models, as formalized by the EI equation. Unified Framework: This research provides a unified, mathematically rigorous framework for integrating Bayesian and non-Bayesian approaches, thereby setting a new benchmark for hybrid predictive systems. Future Research Directions Scalability: Investigating the scalability of the proposed methods, particularly in the context of the ensemble and Bayesian optimization equations, for larger datasets and more models. Real-world Applications: Extending this research to specific domains like healthcare, finance, and natural language processing to assess the practical utility of the proposed methods. Advanced Optimization Techniques: Exploring other optimization techniques that could further improve the efficiency and effectiveness of the proposed hybrid models, perhaps by introducing new mathematical formulations.

Model-based Reinforcement Learning (MBRL) aims to make agents more sample-efficient, adaptive, and explainable by learning an explicit model of the environment. While the capabilities of MBRL agents have significantly improved in recent years, how to best learn the model is still an unresolved question. The majority of MBRL algorithms aim at training the model to make accurate predictions about the environment and subsequently using the model to determine the most rewarding actions. However, recent research has shown that model predictive accuracy is often not correlated with action quality, tracing the root cause to the \emph{objective mismatch} between accurate dynamics model learning and policy optimization of rewards. A number of interrelated solution categories to the objective mismatch problem have emerged as MBRL continues to mature as a research area. In this work, we provide an in-depth survey of these solution categories and propose a taxonomy to foster future research.

This paper proposes a method of abstractive summarization designed to scale to document collections instead of individual documents. Our approach applies a combination of semantic clustering, document size reduction within topic clusters, semantic chunking of a cluster's documents, GPT-based summarization and concatenation, and a combined sentiment and text visualization of each topic to support exploratory data analysis. Statistical comparison of our results to existing state-of-the-art systems BART, BRIO, PEGASUS, and MoCa using ROGUE summary scores showed statistically equivalent performance with BART and PEGASUS on the CNN/Daily Mail test dataset, and with BART on the Gigaword test dataset. This finding is promising since we view document collection summarization as more challenging than individual document summarization. We conclude with a discussion of how issues of scale are

In contrastive learning, two views of an original image generated by different augmentations are considered as a positive pair whose similarity is required to be high. Moreover, two views of two different images are considered as a negative pair, and their similarity is encouraged to be low. Normally, a single similarity measure given by a single projection head is used to evaluate positive and negative sample pairs, respectively. However, due to the various augmentation strategies and varying intra-sample similarity, augmented views from the same image are often not similar. Moreover, due to inter-sample similarity, augmented views of two different images may be more similar than augmented views from the same image. As such, enforcing a high similarity for positive pairs and a low similarity for negative pairs may not always be achievable, and in the case of some pairs, forcing so may be detrimental to the performance. To address this issue, we propose to use multiple projection heads, each producing a separate set of features. Our loss function for pre-training emerges from a solution to the maximum likelihood estimation over head-wise posterior distributions of positive samples given observations. The loss contains the similarity measure over positive and negative pairs, each re-weighted by an individual adaptive temperature that is regularized to prevent ill solutions. Our adaptive multi-head contrastive learning (AMCL) can be applied to and experimentally improves several popular contrastive learning methods such as SimCLR, MoCo and Barlow Twins. Such improvement is consistent under various backbones and linear probing epoches and is more significant when multiple augmentation methods are used.

Like generic multi-task learning, continual learning has the nature of multi-objective optimization, and therefore faces a trade-off between the performance of different tasks. That is, to optimize for the current task distribution, it may need to compromise performance on some previous tasks. This means that there exist multiple models that are Pareto-optimal at different times, each addressing a distinct task performance trade-off. Researchers have discussed how to train particular models to address specific trade-off preferences. However, existing algorithms require training overheads proportional to the number of preferences -- a large burden when there are multiple, possibly infinitely many, preferences. As a response, we propose Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base in the form of a convex hull of model parameter distributions and (2) obtains particular models to address task trade-off preferences with zero-shot. That is, IBCL does not require any additional training overhead to generate preference-addressing models from its knowledge base. We show that models obtained by IBCL have guarantees in identifying the Pareto optimal parameters. Moreover, experiments on standard image classification and NLP tasks support this guarantee. Statistically, IBCL improves average per-task accuracy by at most 23% and peak per-task accuracy by at most 15% with respect to the baseline methods, with steadily near-zero or positive backward transfer. Most importantly, IBCL significantly reduces the training overhead from training 1 model per preference to at most 3 models for all preferences.