Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse structures. Sparsity, in addition, is beneficial in terms of regularization and, thus, to avoid over-fitting. By exploiting Bayesian shrinkage priors, we devise a computationally convenient approach for high-dimensional matrix factorization. The dependence between row and column entities is modeled by inducing flexible sparse patterns within factors. The availability of external information is accounted for in such a way that structures are allowed while not imposed. Inspired by boosting algorithms, we pair the the proposed approach with a numerical strategy relying on a sequential inclusion and estimation of low-rank contributions, with data-driven stopping rule. Practical advantages of the proposed approach are demonstrated by means of a simulation study and the analysis of soccer heatmaps obtained from new generation tracking data.

We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over continuous trajectories conditioned on a scenario, representing what each discrete action would look like if executed in that scenario. While our primary objective is to learn representative action sets, these capabilities combine to produce accurate multimodal trajectory predictions as a byproduct. Although our learned action representations closely resemble semantically meaningful categories (e.g., "go straight", "turn left", etc.), our method is entirely self-supervised and does not utilize any manually generated labels or categories. Our method builds upon recent advances in variational inference and deep unsupervised clustering, resulting in full distribution estimates based on deterministic model evaluations.

The existing methods for trajectory prediction are difficult to describe trajectory of moving objects in complex and uncertain environment accurately. In order to solve this problem, this paper proposes an adaptive trajectory prediction method for moving objects based on variation Gaussian mixture model (VGMM) in dynamic environment (ESATP). Firstly, based on the traditional mixture Gaussian model, we use the approximate variational Bayesian inference method to process the mixture Gaussian distribution in model training procedure. Secondly, variational Bayesian expectation maximization iterative is used to learn the model parameters and prior information is used to get a more precise prediction model. Finally, for the input trajectories, parameter adaptive selection algorithm is used automatically to adjust the combination of parameters. Experiment results perform that the ESATP method in the experiment showed high predictive accuracy, and maintain a high time efficiency. This model can be used in products of mobile vehicle positioning.

Efficient localization plays a vital role in many modern applications of Unmanned Ground Vehicles (UGV) and Unmanned aerial vehicles (UAVs), which would contribute to improved control, safety, power economy, etc. The ubiquitous 5G NR (New Radio) cellular network will provide new opportunities for enhancing localization of UAVs and UGVs. In this paper, we review the radio frequency (RF) based approaches for localization. We review the RF features that can be utilized for localization and investigate the current methods suitable for Unmanned vehicles under two general categories: range-based and fingerprinting. The existing state-of-the-art literature on RF-based localization for both UAVs and UGVs is examined, and the envisioned 5G NR for localization enhancement, and the future research direction are explored.

The publication time of a document carries a relevant information about its semantic content. The Dirichlet-Hawkes process has been proposed to jointly model textual information and publication dynamics. This approach has been used with success in several recent works, and extended to tackle specific challenging problems --typically for short texts or entangled publication dynamics. However, the prior in its current form does not allow for complex publication dynamics. In particular, inferred topics are independent from each other --a publication about finance is assumed to have no influence on publications about politics, for instance. In this work, we develop the Multivariate Powered Dirichlet-Hawkes Process (MPDHP), that alleviates this assumption. Publications about various topics can now influence each other. We detail and overcome the technical challenges that arise from considering interacting topics. We conduct a systematic evaluation of MPDHP on a range of synthetic datasets to define its application domain and limitations. Finally, we develop a use case of the MPDHP on Reddit data. At the end of this article, the interested reader will know how and when to use MPDHP, and when not to.

This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a unified model of syntactic structures in formal grammars. Second, functors compute semantics by turning diagrams into logical, tensor, neural or quantum computation. Third, the resulting functorial models can be composed to form games where equilibria are the solutions of language processing tasks. This framework is implemented as part of DisCoPy, the Python library for computing with string diagrams. We describe the correspondence between categorical, linguistic and computational structures, and demonstrate their applications in compositional natural language processing.

We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic $Q$-Learning (VO$Q$L), based on $Q$-learning and bound its regret assuming completeness and bounded Eluder dimension for the regression function class. As a special case, VO$Q$L achieves $\tilde{O}(d\sqrt{HT}+d^6H^{5})$ regret over $T$ episodes for a horizon $H$ MDP under ($d$-dimensional) linear function approximation, which is asymptotically optimal. Our algorithm incorporates weighted regression-based upper and lower bounds on the optimal value function to obtain this improved regret. The algorithm is computationally efficient given a regression oracle over the function class, making this the first computationally tractable and statistically optimal approach for linear MDPs.

Despite the empirical successes of self-supervised learning (SSL) methods, it is unclear what characteristics of their representations lead to high downstream accuracies. In this work, we characterize properties that SSL representations should ideally satisfy. Specifically, we prove necessary and sufficient conditions such that for any task invariant to given data augmentations, desired probes (e.g., linear or MLP) trained on that representation attain perfect accuracy. These requirements lead to a unifying conceptual framework for improving existing SSL methods and deriving new ones. For contrastive learning, our framework prescribes simple but significant improvements to previous methods such as using asymmetric projection heads. For non-contrastive learning, we use our framework to derive a simple and novel objective. Our resulting SSL algorithms outperform baselines on standard benchmarks, including SwAV+multicrops on linear probing of ImageNet.

The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we propose and analyze the stability of a system under distribution shift, which is defined as the smallest change in the underlying environment that causes the system's performance to deteriorate beyond a permissible threshold. In contrast to standard tail risk measures and distributionally robust losses that require the specification of a plausible magnitude of distribution shift, the stability measure is defined in terms of a more intuitive quantity: the level of acceptable performance degradation. We develop a minimax optimal estimator of stability and analyze its convergence rate, which exhibits a fundamental phase shift behavior. Our characterization of the minimax convergence rate shows that evaluating stability against large performance degradation incurs a statistical cost. Empirically, we demonstrate the practical utility of our stability framework by using it to compare system designs on problems where robustness to distribution shift is critical.

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.