This article investigates the use of Machine Learning and Deep Learning models in multivariate time series analysis within financial markets. It compares small and big data approaches, focusing on their distinct challenges and the benefits of scaling. Traditional methods such as SVMs are contrasted with modern architectures like ConvTimeNet. The results show the importance of using and understanding Big Data in depth in the analysis and prediction of financial time series.

Rovers require knowledge of terrain to plan trajectories that maximize safety and efficiency. Terrain type classification relies on input from human operators or machine learning-based image classification algorithms. However, high level terrain classification is typically not sufficient to prevent incidents such as rovers becoming unexpectedly stuck in a sand trap; in these situations, online rover-terrain interaction data can be leveraged to accurately predict future dynamics and prevent further damage to the rover. This paper presents a meta-learning-based approach to adapt probabilistic predictions of rover dynamics by augmenting a nominal model affine in parameters with a Bayesian regression algorithm (P-ALPaCA). A regularization scheme is introduced to encourage orthogonality of nominal and learned features, leading to interpretable probabilistic estimates of terrain parameters in varying terrain conditions.

Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with diverse cluster definitions, nor do they comply with the integration of constraints when available. In this work, we take inspiration from consensus clustering and assume that a set of clustering models is able to uncover hidden structures in the data. We propose to construct a discriminative ordering through ensemble clustering based on the distance between the connectivity of a clustering model and the consensus matrix. We first validate the proposed method with synthetic scenarios, highlighting that the proposed score ranks the models that best match the consensus first. We then show that this simple ranking score significantly outperforms other scoring methods when comparing sets of different clustering algorithms that are not restricted to a fixed number of clusters and is compatible with clustering constraints.

Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a comprehensive account of IFNs, covering their theoretical foundations, construction methodologies, and diverse applications. Tracing their origins from early network-based models to advanced formulations such as the Triangulated Maximally Filtered Graph (TMFG) and the Maximally Filtered Clique Forest (MFCF), the paper highlights how IFNs address key challenges in high-dimensional data-driven modeling. IFNs and their construction methodologies are intrinsically higher-order networks that generate simplicial complexes-structures that are only now becoming popular in the broader literature. Applications span fields including finance, biology, psychology, and artificial intelligence, where IFNs improve interpretability, computational efficiency, and predictive performance. Special attention is given to their role in graphical modeling, where IFNs enable the estimation of sparse inverse covariance matrices with greater accuracy and scalability than traditional approaches like Graphical LASSO. Finally, the review discusses recent developments that integrate IFNs with machine learning and deep learning, underscoring their potential not only to bridge classical network theory with contemporary data-driven paradigms, but also to shape the architectures of deep learning models themselves.

If a product deviates from its desired properties in the injection moulding process, its root cause analysis can be aided by models that relate the input machine settings with the output quality characteristics. The machine learning models tested in the quality prediction are mostly black boxes; therefore, no direct explanation of their prognosis is given, which restricts their applicability in the quality control. The previously attempted explainability methods are either restricted to tree-based algorithms only or do not emphasize on the fact that some explainability methods can lead to wrong root cause identification of a product's deviation from its desired properties. This study first shows that the interactions among the multiple input machine settings do exist in real experimental data collected as per a central composite design. Then, the model-agnostic explainable AI methods are compared for the first time to show that different explainability methods indeed lead to different feature impact analysis in injection moulding. Moreover, it is shown that the better feature attribution translates to the correct cause identification and actionable insights for the injection moulding process. Being model agnostic, explanations on both random forest and multilayer perceptron are performed for the cause analysis, as both models have the mean absolute percentage error of less than 0.05% on the experimental dataset.

Randomized Uphill Climbing (RUC) is a lightweight, stochastic search heuristic that has delivered state-of-the-art equity "alpha" factors for quantitative hedge funds. I propose to generalize RUC into a model-agnostic feature optimization framework for multivariate time-series forecasting. The core idea is to (i) synthesize candidate feature programs by randomly composing operators from a domain-specific grammar, (ii) score candidates rapidly with inexpensive surrogate models (OLS/Poisson) on rolling windows, and (iii) filter instability via nested cross-validation and information-theoretic shrinkage. By decoupling feature discovery from GPU-heavy deep learning, the method promises faster iteration cycles, lower energy consumption, and greater interpretability. Societal relevance: accurate, transparent forecasting tools empower resource-constrained institutions, energy regulators, climate-risk NGOs--to make data-driven decisions without proprietary black-box models.

This paper introduces ScarceGAN which focuses on identification of extremely rare or scarce samples from multi-dimensional longitudinal telemetry data with small and weak label prior. We specifically address: (i) severe scarcity in positive class, stemming from both underlying organic skew in the data, as well as extremely limited labels; (ii) multi-class nature of the negative samples, with uneven density distributions and partially overlapping feature distributions; and (iii) massively unlabelled data leading to tiny and weak prior on both positive and negative classes, and possibility of unseen or unknown behavior in the unlabelled set, especially in the negative class. Although related to PU learning problems, we contend that knowledge (or lack of it) on the negative class can be leveraged to learn the compliment of it (i.e., the positive class) better in a semi-supervised manner. To this effect, ScarceGAN re-formulates semi-supervised GAN by accommodating weakly labelled multi-class negative samples and the available positive samples. It relaxes the supervised discriminator's constraint on exact differentiation between negative samples by introducing a 'leeway' term for samples with noisy prior. We propose modifications to the cost objectives of discriminator, in supervised and unsupervised path as well as that of the generator. For identifying risky players in skill gaming, this formulation in whole gives us a recall of over 85% (~60% jump over vanilla semi-supervised GAN) on our scarce class with very minimal verbosity in the unknown space. Further ScarceGAN outperforms the recall benchmarks established by recent GAN based specialized models for the positive imbalanced class identification and establishes a new benchmark in identifying one of rare attack classes (0.09%) in the intrusion dataset from the KDDCUP99 challenge.

Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the Random Dot Product Graph (RDPG) model to accommodate weighted graphs, markedly broadening the model's scope to scenarios where edges exhibit heterogeneous weight distributions. We propose a nonparametric weighted (W)RDPG model that assigns a sequence of latent positions to each node. Inner products of these nodal vectors specify the moments of their incident edge weights' distribution via moment-generating functions. In this way, and unlike prior art, the WRDPG can discriminate between weight distributions that share the same mean but differ in other higher-order moments. We derive statistical guarantees for an estimator of the nodal's latent positions adapted from the workhorse adjacency spectral embedding, establishing its consistency and asymptotic normality. We also contribute a generative framework that enables sampling of graphs that adhere to a (prescribed or data-fitted) WRDPG, facilitating, e.g., the analysis and testing of observed graph metrics using judicious reference distributions. The paper is organized to formalize the model's definition, the estimation (or nodal embedding) process and its guarantees, as well as the methodologies for generating weighted graphs, all complemented by illustrative and reproducible examples showcasing the WRDPG's effectiveness in various network analytic applications.

This paper provides a formulation of the particle flow particle filter from the perspective of variational inference. We show that the transient density used to derive the particle flow particle filter follows a time-scaled trajectory of the Fisher-Rao gradient flow in the space of probability densities. The Fisher-Rao gradient flow is obtained as a continuous-time algorithm for variational inference, minimizing the Kullback-Leibler divergence between a variational density and the true posterior density.

This lecture note is intended to prepare early-year master's and PhD students in data science or a related discipline with foundational ideas in machine learning. It starts with basic ideas in modern machine learning with classification as a main target task. These basic ideas include loss formulation, backpropagation, stochastic gradient descent, generalization, model selection as well as fundamental blocks of artificial neural networks. Based on these basic ideas, the lecture note explores in depth the probablistic approach to unsupervised learning, covering directed latent variable models, product of experts, generative adversarial networks and autoregressive models. Finally, the note ends by covering a diverse set of further topics, such as reinforcement learning, ensemble methods and meta-learning. After reading this lecture note, a student should be ready to embark on studying and researching more advanced topics in machine learning and more broadly artificial intelligence.