Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be inferred from observations. Particle filtering can perform such inference given approximate transition and observation models. However, these models are often unknown a priori, yielding a difficult parameter estimation problem since observations jointly carry transition and observation noise. In this work, we consider learning maximum-likelihood parameters using particle methods. Recent methods addressing this problem typically differentiate through time in a particle filter, which requires workarounds to the non-differentiable resampling step, that yield biased or high variance gradient estimates. By contrast, we exploit Fisher's identity to obtain a particle-based approximation of the score function (the gradient of the log likelihood) that yields a low variance estimate while only requiring stepwise differentiation through the transition and observation models. We apply our method to real data collected from autonomous vehicles (AVs) and show that it learns better models than existing techniques and is more stable in training, yielding an effective smoother for tracking the trajectories of vehicles around an AV.

Optimization of directed acyclic graph (DAG) structures has many applications, such as neural architecture search (NAS) and probabilistic graphical model learning. Encoding DAGs into real vectors is a dominant component in most neural-network-based DAG optimization frameworks. Currently, most DAG encoders use an asynchronous message passing scheme which sequentially processes nodes according to the dependency between nodes in a DAG. That is, a node must not be processed until all its predecessors are processed. As a result, they are inherently not parallelizable. In this work, we propose a Parallelizable Attention-based Computation structure Encoder (PACE) that processes nodes simultaneously and encodes DAGs in parallel. We demonstrate the superiority of PACE through encoder-dependent optimization subroutines that search the optimal DAG structure based on the learned DAG embeddings. Experiments show that PACE not only improves the effectiveness over previous sequential DAG encoders with a significantly boosted training and inference speed, but also generates smooth latent (DAG encoding) spaces that are beneficial to downstream optimization subroutines. Our source code is available at \url{https://github.com/zehao-dong/PACE}

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.

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d. settings, the latter in terms of mixing coefficients. Our results suggest RRR might be beneficial over other widely used estimators as confirmed in numerical experiments both for forecasting and mode decomposition.

Sampling is ubiquitous in machine learning methodologies. Due to the growth of large datasets and model complexity, we want to learn and adapt the sampling process while training a representation. Towards achieving this grand goal, a variety of sampling techniques have been proposed. However, most of them either use a fixed sampling scheme or adjust the sampling scheme based on simple heuristics. They cannot choose the best sample for model training in different stages. Inspired by "Think, Fast and Slow" (System 1 and System 2) in cognitive science, we propose a reward-guided sampling strategy called Adaptive Sample with Reward (ASR) to tackle this challenge. To the best of our knowledge, this is the first work utilizing reinforcement learning (RL) to address the sampling problem in representation learning. Our approach optimally adjusts the sampling process to achieve optimal performance. We explore geographical relationships among samples by distance-based sampling to maximize overall cumulative reward. We apply ASR to the long-standing sampling problems in similarity-based loss functions. Empirical results in information retrieval and clustering demonstrate ASR's superb performance across different datasets. We also discuss an engrossing phenomenon which we name as "ASR gravity well" in experiments.

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.

Naive Bayes is a machine learning algorithm that is used for classification tasks. It is based on the idea of applying Bayes' theorem, which describes the probability of an event based on prior knowledge of conditions that might be related to the event. The algorithm makes the assumption that all of the features in the dataset are independent of each other, which is why it is called "naive." This means that the presence or absence of one feature does not affect the probability of the other features. To classify a new data point, the algorithm first calculates the probability of the new data point belonging to each class. It then chooses the class with the highest probability as the predicted class for the new data point. To calculate the probability of a new data point belonging to a given class, the algorithm uses Bayes' theorem, which states that the probability of A given B is equal to the probability of B given A times the probability of A, divided by the probability of B. For example, suppose we have a dataset with two classes: "spam" and "not spam." We can use Bayes' theorem to calculate the probability that a new email belongs to the "spam" class, given that it contains the word "Viagra." We first need to calculate the probability of the word "Viagra" appearing in a "spam" email, and the probability of the word "Viagra" appearing in a "not spam" email. We then multiply these probabilities by the overall probability of the email belonging to the "spam" class, and divide by the probability of the word "Viagra" appearing in any email. Once we have calculated the probabilities for each class, we choose the class with the highest probability as the predicted class for the new data point. Naive Bayes is a simple and effective algorithm for classification tasks, and it can be used with a variety of different types of data.

The unit commitment (UC) problem, which determines operating schedules of generation units to meet demand, is a fundamental task in power systems operation. Existing UC methods using mixed-integer programming are not well-suited to highly stochastic systems. Approaches which more rigorously account for uncertainty could yield large reductions in operating costs by reducing spinning reserve requirements; operating power stations at higher efficiencies; and integrating greater volumes of variable renewables. A promising approach to solving the UC problem is reinforcement learning (RL), a methodology for optimal decision-making which has been used to conquer long-standing grand challenges in artificial intelligence. This thesis explores the application of RL to the UC problem and addresses challenges including robustness under uncertainty; generalisability across multiple problem instances; and scaling to larger power systems than previously studied. To tackle these issues, we develop guided tree search, a novel methodology combining model-free RL and model-based planning. The UC problem is formalised as a Markov decision process and we develop an open-source environment based on real data from Great Britain's power system to train RL agents. In problems of up to 100 generators, guided tree search is shown to be competitive with deterministic UC methods, reducing operating costs by up to 1.4\%. An advantage of RL is that the framework can be easily extended to incorporate considerations important to power systems operators such as robustness to generator failure, wind curtailment or carbon prices. When generator outages are considered, guided tree search saves over 2\% in operating costs as compared with methods using conventional $N-x$ reserve criteria.

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.