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.

In this note we present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference, which we refer to as Bayesian Renormalization. The main insight of Bayesian Renormalization is that the Fisher metric defines a correlation length that plays the role of an emergent RG scale quantifying the distinguishability between nearby points in the space of probability distributions. This RG scale can be interpreted as a proxy for the maximum number of unique observations that can be made about a given system during a statistical inference experiment. The role of the Bayesian Renormalization scheme is subsequently to prepare an effective model for a given system up to a precision which is bounded by the aforementioned scale. In applications of Bayesian Renormalization to physical systems, the emergent information theoretic scale is naturally identified with the maximum energy that can be probed by current experimental apparatus, and thus Bayesian Renormalization coincides with ordinary renormalization. However, Bayesian Renormalization is sufficiently general to apply even in circumstances in which an immediate physical scale is absent, and thus provides an ideal approach to renormalization in data science contexts. To this end, we provide insight into how the Bayesian Renormalization scheme relates to existing methods for data compression and data generation such as the information bottleneck and the diffusion learning paradigm. We conclude by designing an explicit form of Bayesian Renormalization inspired by Wilson's momentum shell renormalization scheme in Quantum Field Theory. We apply this Bayesian Renormalization scheme to a simple Neural Network and verify the sense in which it organizes the parameters of the model according to a hierarchy of information theoretic importance.

Causal discovery (CD) from time-varying data is important in neuroscience, medicine, and machine learning. Techniques for CD encompass randomized experiments, which are generally unbiased but expensive, and algorithms such as Granger causality, conditional-independence-based, structural-equation-based, and score-based methods that are only accurate under strong assumptions made by human designers. However, as demonstrated in other areas of machine learning, human expertise is often not entirely accurate and tends to be outperformed in domains with abundant data. In this study, we examine whether we can enhance domain-specific causal discovery for time series using a data-driven approach. Our findings indicate that this procedure significantly outperforms human-designed, domain-agnostic causal discovery methods, such as Mutual Information, VAR-LiNGAM, and Granger Causality on the MOS 6502 microprocessor, the NetSim fMRI dataset, and the Dream3 gene dataset. We argue that, when feasible, the causality field should consider a supervised approach in which domain-specific CD procedures are learned from extensive datasets with known causal relationships, rather than being designed by human specialists. Our findings promise a new approach toward improving CD in neural and medical data and for the broader machine learning community.