Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform simple independence tests in each stratum, and combine the results. Unfortunately, the statistical power of this approach degrades rapidly as the number of conditioning variables increases. Here we propose a simple unified CI test for ordinal and categorical data that maintains reasonable calibration and power in high dimensions. We show that our test outperforms existing baselines in model testing and structure learning for dense directed graphical models while being comparable for sparse models. Our approach could be attractive for causal model testing because it is easy to implement, can be used with non-parametric or parametric probability models, has the symmetry property, and has reasonable computational requirements.

We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with additive Gaussian noise and consider interventions that perturb their targets while maintaining the causal relationships in the system. Different models may entail the same distributions, offering competing causal explanations for the given observations. We fully characterize this equivalence class and offer identifiability results, which we use to derive a greedy algorithm called GnIES to recover the equivalence class of the data-generating model without knowledge of the intervention targets. In addition, we develop a novel procedure to generate semi-synthetic data sets with known causal ground truth but distributions closely resembling those of a real data set of choice. We leverage this procedure and evaluate the performance of GnIES on synthetic, real, and semi-synthetic data sets. Despite the strong Gaussian distributional assumption, GnIES is robust to an array of model violations and competitive in recovering the causal structure in small- to large-sample settings. We provide, in the Python packages "gnies" and "sempler", implementations of GnIES and our semi-synthetic data generation procedure.

A new form of ML knowledge representation with high generalization power is developed and implemented numerically. Initial $\mathit{IN}$ attributes and $\mathit{OUT}$ class label are transformed into the corresponding Hilbert spaces by considering localized wavefunctions. A partially unitary operator optimally converting a state from $\mathit{IN}$ Hilbert space into $\mathit{OUT}$ Hilbert space is then built from an optimization problem of transferring maximal possible probability from $\mathit{IN}$ to $\mathit{OUT}$, this leads to the formulation of a new algebraic problem. Constructed Knowledge Generalizing Operator $\mathcal{U}$ can be considered as a $\mathit{IN}$ to $\mathit{OUT}$ quantum channel; it is a partially unitary rectangular matrix of the dimension $\mathrm{dim}(\mathit{OUT}) \times \mathrm{dim}(\mathit{IN})$ transforming operators as $A^{\mathit{OUT}}=\mathcal{U} A^{\mathit{IN}} \mathcal{U}^{\dagger}$. Whereas only operator $\mathcal{U}$ projections squared are observable $\left\langle\mathit{OUT}|\mathcal{U}|\mathit{IN}\right\rangle^2$ (probabilities), the fundamental equation is formulated for the operator $\mathcal{U}$ itself. This is the reason of high generalizing power of the approach; the situation is the same as for the Schr\"{o}dinger equation: we can only measure $\psi^2$, but the equation is written for $\psi$ itself.

This thesis considers sequential decision problems, where the loss/reward incurred by selecting an action may not be inferred from observed feedback. A major part of this thesis focuses on the unsupervised sequential selection problem, where one can not infer the loss incurred for selecting an action from observed feedback. We also introduce a new setup named Censored Semi Bandits, where the loss incurred for selecting an action can be observed under certain conditions. Finally, we study the channel selection problem in the communication networks, where the reward for an action is only observed when no other player selects that action to play in the round. These problems find applications in many fields like healthcare, crowd-sourcing, security, adaptive resource allocation, among many others. This thesis aims to address the above-described sequential decision problems by exploiting specific structures these problems exhibit. We develop provably optimal algorithms for each of these setups with weak feedback and validate their empirical performance on different problem instances derived from synthetic and real datasets.

Deep generative models parametrized up to a normalizing constant (e.g. energy-based models) are difficult to train by maximizing the likelihood of the data because the likelihood and/or gradients thereof cannot be explicitly or efficiently written down. Score matching is a training method, whereby instead of fitting the likelihood $\log p(x)$ for the training data, we instead fit the score function $\nabla_x \log p(x)$ -- obviating the need to evaluate the partition function. Though this estimator is known to be consistent, its unclear whether (and when) its statistical efficiency is comparable to that of maximum likelihood -- which is known to be (asymptotically) optimal. We initiate this line of inquiry in this paper, and show a tight connection between statistical efficiency of score matching and the isoperimetric properties of the distribution being estimated -- i.e. the Poincar\'e, log-Sobolev and isoperimetric constant -- quantities which govern the mixing time of Markov processes like Langevin dynamics. Roughly, we show that the score matching estimator is statistically comparable to the maximum likelihood when the distribution has a small isoperimetric constant. Conversely, if the distribution has a large isoperimetric constant -- even for simple families of distributions like exponential families with rich enough sufficient statistics -- score matching will be substantially less efficient than maximum likelihood. We suitably formalize these results both in the finite sample regime, and in the asymptotic regime. Finally, we identify a direct parallel in the discrete setting, where we connect the statistical properties of pseudolikelihood estimation with approximate tensorization of entropy and the Glauber dynamics.

Multi-class ensemble classification remains a popular focus of investigation within the research community. The popularization of cloud services has sped up their adoption due to the ease of deploying large-scale machine-learning models. It has also drawn the attention of the industrial sector because of its ability to identify common problems in production. However, there are challenges to conform an ensemble classifier, namely a proper selection and effective training of the pool of classifiers, the definition of a proper architecture for multi-class classification, and uncertainty quantification of the ensemble classifier. The robustness and effectiveness of the ensemble classifier lie in the selection of the pool of classifiers, as well as in the learning process. Hence, the selection and the training procedure of the pool of classifiers play a crucial role. An (ensemble) classifier learns to detect the classes that were used during the supervised training. However, when injecting data with unknown conditions, the trained classifier will intend to predict the classes learned during the training. To this end, the uncertainty of the individual and ensemble classifier could be used to assess the learning capability. We present a novel approach for novel detection using ensemble classification and evidence theory. A pool selection strategy is presented to build a solid ensemble classifier. We present an architecture for multi-class ensemble classification and an approach to quantify the uncertainty of the individual classifiers and the ensemble classifier. We use uncertainty for the anomaly detection approach. Finally, we use the benchmark Tennessee Eastman to perform experiments to test the ensemble classifier's prediction and anomaly detection capabilities.

In this article, we aim to provide a literature review of different formulations and approaches to continual reinforcement learning (RL), also known as lifelong or non-stationary RL. We begin by discussing our perspective on why RL is a natural fit for studying continual learning. We then provide a taxonomy of different continual RL formulations by mathematically characterizing two key properties of non-stationarity, namely, the scope and driver non-stationarity. This offers a unified view of various formulations. Next, we review and present a taxonomy of continual RL approaches. We go on to discuss evaluation of continual RL agents, providing an overview of benchmarks used in the literature and important metrics for understanding agent performance. Finally, we highlight open problems and challenges in bridging the gap between the current state of continual RL and findings in neuroscience. While still in its early days, the study of continual RL has the promise to develop better incremental reinforcement learners that can function in increasingly realistic applications where non-stationarity plays a vital role. These include applications such as those in the fields of healthcare, education, logistics, and robotics.

My client, a world leader in the defence sector, requires an Machine Learning Algorithm Developer to join them in Bristol and work as part of a team on the development and evaluation of state-of-the-art algorithms for the guidance, control and navigation of their missile and weapon systems.
 
The Machine Learning Algorithm Developer will work within a team of Intelligent Systems, Autonomous Systems and Command and Control Engineers to develop and evaluate state-of-the-art algorithms across a range of domains from on-board, autonomous decision making to off-board algorithms. The work will involve the research, development, test, evaluation and implementation of algorithms that integrate into complex guided weapon systems products.
 
Algorithms are central to the design of sophisticated guided weapon systems products. These algorithms are developed throughout the lifecycle of the product and include research studies to investigate algorithms for future developments.

Machine Learning Algorithm Developers are involved in the lifecycle of projects, playing a pivotal role in our product developments including:
 
Technical development of specific algorithms or studies for key programmes.Feasibility studies, algorithm design and trade-off studies, preparing trials, trials analysis and reporting, defining architecture, validating algorithms and models.Technical assessments and investigations into a full range of issues and problems and prepare and develop solutions either solely or as a member of a project team.Engaging with the algorithm users, understanding and responding to their needs and ensure that the algorithms are fit for purpose. 
You will gain exposure to a range of other related subject areas e.g. Simulation and Modelling, Software, Hardware-in-the Loop, Systems Design & Validation, Seekers & Sensors, Datalinks and Technical Quality and will be exposed to cutting-edge technological innovations, playing a meaningful role through the development of complex weapon systems.
 
To be considered for this role, applicants will ideally have completed (or be soon to complete) a PhD level in a related area with a good degree in a subject with strong mathematical content and programming skills e.g. Engineering, Mathematics, Physics, Computer Science, Information Engineering. 
 
You will have previous experience in the development and practical application of algorithms, with experience in some of the following:
 
Robotics, data fusion, tracking/estimation, pattern discovery & recognition, statistical inference, optimisation and machine/deep learning algorithms along with real-time implementation, and/or validation & verification.
 
You will also have experience in some of the following: Matlab, Simulink, Stateflow, Python including PyTorch, TensorFlow, Open AI-Gym/Universe, Model Based Design.
 
Specific knowledge or experience in any of these areas would also be ideal:
 
Robotics, guidance and autonomous decision making, e.g. Routing and motion/trajectory planning, optimisation, co-ordinated guidance and control, decision theory, MDPs/POMDPs, specialist systems, game theory, decision support systems, multi-agent systemsData fusion and state estimation/tracking algorithms e.g. Kalman Filtering, multiple-model tracking methods, particle filters, grid-based estimation methods, Multi-Object-Multi-Sensor Fusion, data-association, random finite sets, Bayesian belief networks, Dempster-Shafer theory of evidenceMachine Learning for regression and pattern recognition/discovery problems e.g. Gaussian processes, latent variable methods, support vector machines, probabilistic/statistical models, neural networks, Bayesian inference, random-forests, novelty detection, clusteringDeep Learning e.g. Deep reinforcement learning, Monte-Carlo tree search, deep regression/classification, deep embeddings, recurrent Networks, natural language processingComputer Vision algorithms e.g. Structure from motion, image Based navigation, SLAM, pose estimation/recovery 
Machine Learning Algorithm Developer
Bristol
Salary £35-50k plus benefits DOE
 
Key Skills: Intelligent Systems Engineer, Intelligent Autonomous Systems Engineer, IAS Engineer, PhD, Mathematics, Algorithms, Programming, Robotics, Autonomous Decision Making, Machine Learning, Deep Learning, Data Fusion, Pattern Discovery, Pattern Recognition, Computer Vision, Machine Vision, Matlab, Simulink, Stateflow, Python, PyTorch
   
Due to the nature of work undertaken at our client's site, incumbents of these positions are required to meet special nationality rules and therefore these vacancies are only open to sole British Citizens. Applicants who meet these criteria will also be required to undergo security clearance vetting, if not already security cleared to a minimum SC level.
 
Electus Recruitment Solutions provides specialist engineering and technical recruitment solutions to a number of high technology industries. We thank you for your interest in this vacancy. If you don't hear from us within 7 working days please presume your application has been unsuccessful on this occasion. You are of course free to resubmit your CV/details in the future and we shall assess your suitability at that time. 
   
This role is a PERMANENT position

Quadrotors with the ability to perch on moving inclined surfaces can save energy and extend their travel distance by leveraging ground vehicles. Achieving dynamic perching places high demands on the performance of trajectory planning and terminal state accuracy in SE(3). However, in the perching process, uncertainties in target surface prediction, tracking control and external disturbances may cause trajectory planning failure or lead to unacceptable terminal errors. To address these challenges, we first propose a trajectory planner that considers adaptation to uncertainties in target prediction and tracking control. To facilitate this work, the reachable set of quadrotors' states is first analyzed. The states whose reachable sets possess the largest coverage probability for uncertainty targets, are defined as optimal waypoints. Subsequently, an approach to seek local optimal waypoints for static and moving uncertainty targets is proposed. A real-time trajectory planner based on optimized waypoints is developed accordingly. Secondly, thrust regulation is also implemented in the terminal attitude tracking stage to handle external disturbances. When a quadrotor's attitude is commanded to align with target surfaces, the thrust is optimized to minimize terminal errors. This makes the terminal position and velocity be controlled in closed-loop manner. Therefore, the resistance to disturbances and terminal accuracy is improved. Extensive simulation experiments demonstrate that our methods can improve the accuracy of terminal states under uncertainties. The success rate is approximately increased by $50\%$ compared to the two-end planner without thrust regulation. Perching on the rear window of a car is also achieved using our proposed heterogeneous cooperation system outdoors. This validates the feasibility and practicality of our methods.

We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation which we dub Bayesian Diffusion. Identifying the features that define Bayesian Diffusion, and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.