Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

Locally stationary processes (LSPs) provide a robust framework for modeling time-varying phenomena, allowing for smooth variations in statistical properties such as mean and variance over time. In this paper, we address the estimation of the conditional probability distribution of LSPs using Nadaraya-Watson (NW) type estimators. The NW estimator approximates the conditional distribution of a target variable given covariates through kernel smoothing techniques. We establish the convergence rate of the NW conditional probability estimator for LSPs in the univariate setting under the Wasserstein distance and extend this analysis to the multivariate case using the sliced Wasserstein distance. Theoretical results are supported by numerical experiments on both synthetic and real-world datasets, demonstrating the practical usefulness of the proposed estimators.

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the P\'olya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.

Advancements in artificial intelligence, machine learning, and deep learning have catalyzed the transformation of big data analytics and management into pivotal domains for research and application. This work explores the theoretical foundations, methodological advancements, and practical implementations of these technologies, emphasizing their role in uncovering actionable insights from massive, high-dimensional datasets. The study presents a systematic overview of data preprocessing techniques, including data cleaning, normalization, integration, and dimensionality reduction, to prepare raw data for analysis. Core analytics methodologies such as classification, clustering, regression, and anomaly detection are examined, with a focus on algorithmic innovation and scalability. Furthermore, the text delves into state-of-the-art frameworks for data mining and predictive modeling, highlighting the role of neural networks, support vector machines, and ensemble methods in tackling complex analytical challenges. Special emphasis is placed on the convergence of big data with distributed computing paradigms, including cloud and edge computing, to address challenges in storage, computation, and real-time analytics. The integration of ethical considerations, including data privacy and compliance with global standards, ensures a holistic perspective on data management. Practical applications across healthcare, finance, marketing, and policy-making illustrate the real-world impact of these technologies. Through comprehensive case studies and Python-based implementations, this work equips researchers, practitioners, and data enthusiasts with the tools to navigate the complexities of modern data analytics. It bridges the gap between theory and practice, fostering the development of innovative solutions for managing and leveraging data in the era of artificial intelligence.

Understanding how galaxies form and evolve is at the heart of modern astronomy. With the advent of large-scale surveys and simulations, remarkable progress has been made in the last few decades. Despite this, the physical processes behind the phenomena, and particularly their importance, remain far from known, as correlations have primarily been established rather than the underlying causality. We address this challenge by applying the causal inference framework. Specifically, we tackle the fundamental open question of whether galaxy formation and evolution depends more on nature (i.e., internal processes) or nurture (i.e., external processes), by estimating the causal effect of environment on star-formation rate in the IllustrisTNG simulations. To do so, we develop a comprehensive causal model and employ cutting-edge techniques from epidemiology to overcome the long-standing problem of disentangling nature and nurture. We find that the causal effect is negative and substantial, with environment suppressing the SFR by a maximal factor of $\sim100$. While the overall effect at $z=0$ is negative, in the early universe, environment is discovered to have a positive impact, boosting star formation by a factor of $\sim10$ at $z\sim1$ and by even greater amounts at higher redshifts. Furthermore, we show that: (i) nature also plays an important role, as ignoring it underestimates the causal effect in intermediate-density environments by a factor of $\sim2$, (ii) controlling for the stellar mass at a snapshot in time, as is common in the literature, is not only insufficient to disentangle nature and nurture but actually has an adverse effect, though (iii) stellar mass is an adequate proxy of the effects of nature. Finally, this work may prove a useful blueprint for extracting causal insights in other fields that deal with dynamical systems with closed feedback loops, such as the Earth's climate.

We introduce a causal modeling framework that captures the input-output behavior of predictive models (e.g., machine learning models) by representing it using causal graphs. The framework enables us to define and identify features that directly cause the predictions, which has broad implications for data collection and model evaluation. We show two assumptions under which the direct causes can be discovered from data, one of which further simplifies the discovery process. In addition to providing sound and complete algorithms, we propose an optimization technique based on an independence rule that can be integrated with the algorithms to speed up the discovery process both theoretically and empirically.

The concept of abstraction has been independently developed both in the context of AI Planning and discounted Markov Decision Processes (MDPs). However, the way abstractions are built and used in the context of Planning and MDPs is different even though lots of commonalities can be highlighted. To this day there is no work trying to relate and unify the two fields on the matter of abstractions unraveling all the different assumptions and their effect on the way they can be used. Therefore, in this paper we aim to do so by looking at projection abstractions in Planning through the lenses of discounted MDPs. Starting from a projection abstraction built according to Classical or Probabilistic Planning techniques, we will show how the same abstraction can be obtained under the abstraction frameworks available for discounted MDPs. Along the way, we will focus on computational as well as representational advantages and disadvantages of both worlds pointing out new research directions that are of interest for both fields.

Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM, with a focus on the effect of the unit priors on learning efficiency. We consider a parametric class of priors that interpolate between continuous (Gaussian) and binary variables. This approach models various possible choices of visible units, hidden units, and weights for both the teacher and student RBMs. By analyzing the phase diagram of the posterior distribution in both the Bayes optimal and mismatched regimes, we demonstrate the existence of a triple point that defines the critical dataset size necessary for learning through generalization. The critical size is strongly influenced by the properties of the teacher, and thus the data, but is unaffected by the properties of the student RBM. Nevertheless, a prudent choice of student priors can facilitate training by expanding the so-called signal retrieval region, where the machine generalizes effectively.

Learning quantum states is a crucial task for realizing the potential of quantum information technology. Recently, neural approaches have emerged as promising methods for learning quantum states. We propose a meta-learning model that employs reinforcement learning (RL) to optimize the process of learning quantum states. For learning quantum states, our scheme trains a Hardware efficient ansatz with a blackbox optimization algorithm, called evolution strategy (ES). To enhance the efficiency of ES, a RL agent dynamically adjusts the hyperparameters of ES. To facilitate the RL training, we introduce an action repetition strategy inspired by curriculum learning. The RL agent significantly improves the sample efficiency of learning random quantum states, and achieves infidelity scaling close to the Heisenberg limit. We showcase that the RL agent trained using 3-qubit states can be generalized to learning up to 5-qubit states. These results highlight the utility of RL-driven meta-learning to enhance the efficiency and generalizability of learning quantum states. Our approach can be applicable to improve quantum control, quantum optimization, and quantum machine learning.

Autonomous agents operating in adversarial scenarios face a fundamental challenge: while they may know their adversaries' high-level objectives, such as reaching specific destinations within time constraints, the exact policies these adversaries will employ remain unknown. Traditional approaches address this challenge by treating the adversary's state as a partially observable element, leading to a formulation as a Partially Observable Markov Decision Process (POMDP). However, the induced belief-space dynamics in a POMDP require knowledge of the system's transition dynamics, which, in this case, depend on the adversary's unknown policy. Our key observation is that while an adversary's exact policy is unknown, their behavior is necessarily constrained by their mission objectives and the physical environment, allowing us to characterize the space of possible behaviors without assuming specific policies. In this paper, we develop Task-Aware Behavior Fields (TAB-Fields), a representation that captures adversary state distributions over time by computing the most unbiased probability distribution consistent with known constraints. We construct TAB-Fields by solving a constrained optimization problem that minimizes additional assumptions about adversary behavior beyond mission and environmental requirements. We integrate TAB-Fields with standard planning algorithms by introducing TAB-conditioned POMCP, an adaptation of Partially Observable Monte Carlo Planning. Through experiments in simulation with underwater robots and hardware implementations with ground robots, we demonstrate that our approach achieves superior performance compared to baselines that either assume specific adversary policies or neglect mission constraints altogether. Evaluation videos and code are available at https://tab-fields.github.io.