Extracting governing physics from data is a key challenge in many areas of science and technology. The existing techniques for equations discovery are dependent on both input and state measurements; however, in practice, we only have access to the output measurements only. We here propose a novel framework for learning governing physics of dynamical system from output only measurements; this essentially transfers the physics discovery problem from the deterministic to the stochastic domain. The proposed approach models the input as a stochastic process and blends concepts of stochastic calculus, sparse learning algorithms, and Bayesian statistics. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data. The resulting model is highly efficient and works with sparse, noisy, and incomplete output measurements. The efficacy and robustness of the proposed approach is illustrated on several numerical examples involving both complete and partial state measurements. The results obtained indicate the potential of the proposed approach in identifying governing physics from output only measurement.

Learning predictors that do not rely on spurious correlations involves building causal representations. However, learning such a representation is very challenging. We, therefore, formulate the problem of learning a causal representation from high dimensional data and study causal recovery with synthetic data. This work introduces a latent variable decoder model, Decoder BCD, for Bayesian causal discovery and performs experiments in mildly supervised and unsupervised settings. We present a series of synthetic experiments to characterize important factors for causal discovery and show that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters of linear Gaussian additive noise latent structural causal models.

We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal probabilities in its dual normal factor graph. The mapping is based on the Fourier transform of the local factors of the models. Details of the mapping are provided for the Ising model, where it is proved that the local extrema of the fixed points are attained at the phase transition of the two-dimensional nearest-neighbor Ising model. The results are further extended to the Potts model, to the clock model, and to Gaussian Markov random fields. By employing the mapping, we can transform simultaneously all the estimated marginal probabilities from the dual domain to the primal domain (and vice versa), which is advantageous if estimating the marginals can be carried out more efficiently in the dual domain. An example of particular significance is the ferromagnetic Ising model in a positive external magnetic field. For this model, there exists a rapidly mixing Markov chain (called the subgraphs--world process) to generate configurations in the dual normal factor graph of the model. Our numerical experiments illustrate that the proposed procedure can provide more accurate estimates of marginal probabilities of a global probability mass function in various settings.

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus enabling the computation of the exponential convergence rates for the events of interest on the iterates. Relevant applications include error exponents in distributed hypothesis testing, rates of convergence of beliefs in social learning, and inaccuracy rates in distributed estimation. The bounds on the rate function have a very particular form at each node: they are constructed as the convex envelope between the rate function of the hypothetical fusion center and the rate function corresponding to a certain topological mode of the node's presence. We further show tightness of the discovered bounds for several cases, such as pendant nodes and regular networks, thus establishing the first proof of the large deviations principle for consensus+innovations and social learning in random networks.

We consider learning Nash equilibria in two-player zero-sum Markov Games with nonlinear function approximation, where the action-value function is approximated by a function in a Reproducing Kernel Hilbert Space (RKHS). The key challenge is how to do exploration in the high-dimensional function space. We propose a novel online learning algorithm to find a Nash equilibrium by minimizing the duality gap. At the core of our algorithms are upper and lower confidence bounds that are derived based on the principle of optimism in the face of uncertainty. We prove that our algorithm is able to attain an $O(\sqrt{T})$ regret with polynomial computational complexity, under very mild assumptions on the reward function and the underlying dynamic of the Markov Games. We also propose several extensions of our algorithm, including an algorithm with Bernstein-type bonus that can achieve a tighter regret bound, and another algorithm for model misspecification that can be applied to neural function approximation.

We consider the problem of characterizing Bayesian networks up to unconditional equivalence, i.e., when directed acyclic graphs (DAGs) have the same set of unconditional d-separation statements. Each unconditional equivalence class (UEC) is uniquely represented with an undirected graph whose clique structure encodes the members of the class. Via this structure, we provide a transformational characterization of unconditional equivalence; i.e., we show that two DAGs are in the same UEC if and only if one can be transformed into the other via a finite sequence of specified moves. We also extend this characterization to the essential graphs representing the Markov equivalence classes (MECs) in the UEC. UECs partition the space of MECs and are easily estimable from marginal independence tests. Thus, a characterization of unconditional equivalence has applications in methods that involve searching the space of MECs of Bayesian networks. Keywords: unconditional equivalence; marginal independence structure; undirected graphs; directed acyclic graphs; chain graphs; Markov equivalence.

Abstract-- The visual analytics community has proposed several user modeling algorithms to capture and analyze users' interaction behavior in order to assist users in data exploration and insight generation. For example, some can detect exploration biases while others can predict data points that the user will interact with before that interaction occurs. Researchers believe this collection of algorithms can help create more intelligent visual analytics tools. However, the community lacks a rigorous evaluation and comparison of these existing techniques. As a result, there is limited guidance on which method to use and when. Our paper seeks to fill in this missing gap by comparing and ranking eight user modeling algorithms based on their performance on a diverse set of four user study datasets. We analyze exploration bias detection, data interaction prediction, and algorithmic complexity, among other measures. Based on our findings, we highlight open challenges and new directions for analyzing user interactions and visualization provenance. After surveying the body of work, we selected seven proposed Researchers in the visualization community have long viewed interaction techniques and standardized their input and output specifications to as an analytic discourse between the analyst and the visualization account for a variety of datasets. In addition to the selected models, system [40].

Score-based generative models (SGMs) synthesize new data samples from Gaussian white noise by running a time-reversed Stochastic Differential Equation (SDE) whose drift coefficient depends on some probabilistic score. The discretization of such SDEs typically requires a large number of time steps and hence a high computational cost. This is because of ill-conditioning properties of the score that we analyze mathematically. We show that SGMs can be considerably accelerated, by factorizing the data distribution into a product of conditional probabilities of wavelet coefficients across scales. The resulting Wavelet Score-based Generative Model (WSGM) synthesizes wavelet coefficients with the same number of time steps at all scales, and its time complexity therefore grows linearly with the image size. This is proved mathematically over Gaussian distributions, and shown numerically over physical processes at phase transition and natural image datasets.

Despite echo chambers in social media have been under considerable scrutiny, general models for their detection and analysis are missing. In this work, we aim to fill this gap by proposing a probabilistic generative model that explains social media footprints -- i.e., social network structure and propagations of information -- through a set of latent communities, characterized by a degree of echo-chamber behavior and by an opinion polarity. Specifically, echo chambers are modeled as communities that are permeable to pieces of information with similar ideological polarity, and impermeable to information of opposed leaning: this allows discriminating echo chambers from communities that lack a clear ideological alignment. To learn the model parameters we propose a scalable, stochastic adaptation of the Generalized Expectation Maximization algorithm, that optimizes the joint likelihood of observing social connections and information propagation. Experiments on synthetic data show that our algorithm is able to correctly reconstruct ground-truth latent communities with their degree of echo-chamber behavior and opinion polarity. Experiments on real-world data about polarized social and political debates, such as the Brexit referendum or the COVID-19 vaccine campaign, confirm the effectiveness of our proposal in detecting echo chambers. Finally, we show how our model can improve accuracy in auxiliary predictive tasks, such as stance detection and prediction of future propagations.

Load balancing (LB) is a challenging issue in the hybrid light fidelity (LiFi) and wireless fidelity (WiFi) networks (HLWNets), due to the nature of heterogeneous access points (APs). Machine learning has the potential to provide a complexity-friendly LB solution with near-optimal network performance, at the cost of a training process. The state-of-the-art (SOTA) learning-aided LB methods, however, need retraining when the network environment (especially the number of users) changes, significantly limiting its practicability. In this paper, a novel deep neural network (DNN) structure named adaptive target-condition neural network (A-TCNN) is proposed, which conducts AP selection for one target user upon the condition of other users. Also, an adaptive mechanism is developed to map a smaller number of users to a larger number through splitting their data rate requirements, without affecting the AP selection result for the target user. This enables the proposed method to handle different numbers of users without the need for retraining. Results show that A-TCNN achieves a network throughput very close to that of the testing dataset, with a gap less than 3%. It is also proven that A-TCNN can obtain a network throughput comparable to two SOTA benchmarks, while reducing the runtime by up to three orders of magnitude.