Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly assume noisy labels in different pixels are \textit{i.i.d}. However, segmentation label noise usually has strong spatial correlation and has prominent bias in distribution. In this paper, we propose a novel Markov model for segmentation noisy annotations that encodes both spatial correlation and bias. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.

Malnutrition and dehydration are strongly associated with increased cognitive and functional decline in people living with dementia (PLWD), as well as an increased rate of hospitalisations in comparison to their healthy counterparts. Extreme changes in eating and drinking behaviours can often lead to malnutrition and dehydration, accelerating the progression of cognitive and functional decline and resulting in a marked reduction in quality of life. Unfortunately, there are currently no established methods by which to objectively detect such changes. Here, we present the findings of an extensive quantitative analysis conducted on in-home monitoring data collected from 73 households of PLWD using Internet of Things technologies. The Coronavirus 2019 (COVID-19) pandemic has previously been shown to have dramatically altered the behavioural habits, particularly the eating and drinking habits, of PLWD. Using the COVID-19 pandemic as a natural experiment, we conducted linear mixed-effects modelling to examine changes in mean kitchen activity within a subset of 21 households of PLWD that were continuously monitored for 499 days. We report an observable increase in day-time kitchen activity and a significant decrease in night-time kitchen activity (t(147) = -2.90, p < 0.001). We further propose a novel analytical approach to detecting changes in behaviours of PLWD using Markov modelling applied to remote monitoring data as a proxy for behaviours that cannot be directly measured. Together, these results pave the way to introduce improvements into the monitoring of PLWD in naturalistic settings and for shifting from reactive to proactive care.

When has an agent converged? Standard models of the reinforcement learning problem give rise to a straightforward definition of convergence: An agent converges when its behavior or performance in each environment state stops changing. However, as we shift the focus of our learning problem from the environment's state to the agent's state, the concept of an agent's convergence becomes significantly less clear. In this paper, we propose two complementary accounts of agent convergence in a framing of the reinforcement learning problem that centers around bounded agents. The first view says that a bounded agent has converged when the minimal number of states needed to describe the agent's future behavior cannot decrease. The second view says that a bounded agent has converged just when the agent's performance only changes if the agent's internal state changes. We establish basic properties of these two definitions, show that they accommodate typical views of convergence in standard settings, and prove several facts about their nature and relationship. We take these perspectives, definitions, and analysis to bring clarity to a central idea of the field.

Social robots are robots that are designed specifically to interact with their human users [14] for example by using spoken dialogue. For social robots, the interaction with humans plays a crucial role [7, 27], for example in the context of elderly care [15] or education [9]. Robots that use speech as a main mode of interaction do not only need to understand the user's utterances, but also need to select appropriate responses given the context. Dialogue management (DM), according to Traum and Larsson [88], is the part of a dialogue system that performs four key functions: 1) it maintains and updates the context of the dialogue, 2) it includes the context of the utterance for interpretation of input, 3) it selects the timing and content of the next utterance, and 4) it coordinates with (non-)dialogue modules. In spoken dialogue systems, the dialogue manager receives its input from a natural language understanding (NLU) module and forwards its results to a natural language generation (NLG) module, which then generates the output (see Figure 1). In contrast to general DM, DM in human-robot interaction (HRI) has to also consider and manage the complexity added by social robots (see Figure 1). The concentric circles of the figure describe decisions that have to be made when designing a dialogue manager for human-robot interaction. From each circle, one or more options can be chosen and combined with each other.

The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a history of observations and actions over time. Recent studies have shown that the sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs). Despite these advancements, existing approaches typically involve oracles or steps that are not computationally efficient. On the other hand, the upper confidence bound (UCB) based approaches, which have served successfully as computationally efficient methods in bandits and MDPs, have not been investigated for more general PSRs, due to the difficulty of optimistic bonus design in these more challenging settings. This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. We further characterize the sample complexity bounds for our designed UCB-type algorithms for both online and offline PSRs. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational efficiency, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.

Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be computed piecewise in terms of the component processes. We study the structure of this compositional rule, noting that it relates to the lens pattern in functional programming. Working in a suitably general axiomatic presentation of a category of Markov kernels, we see how we can think of Bayesian inversion as a particular instance of a state-dependent morphism in a fibred category. We discuss the compositional nature of this, formulated as a functor on the underlying category and explore how this can used for a more type-driven approach to statistical inference.

The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample statistical asymptotics of SGAs via a joint step-size--sample-size scaling limit. We show that iterate averaging with a large fixed step size is robust to the choice of tuning parameters and asymptotically has covariance proportional to that of the MLE sampling distribution. We also prove a Bernstein--von Mises-like theorem to guide tuning, including for generalized posteriors that are robust to model misspecification. Numerical experiments validate our results and recommendations in realistic finite-sample regimes. Our work lays the foundation for a systematic analysis of other stochastic gradient Markov chain Monte Carlo algorithms for a wide range of models.

Item Response Theory (IRT) is a well known method for assessing responses from humans in education and psychology. In education, IRT is used to infer student abilities and characteristics of test items from student responses. Interactions with students are expensive, calling for methods that efficiently gather information for inferring student abilities. Methods based on Optimal Experimental Design (OED) are computationally costly, making them inapplicable for interactive applications. In response, we propose incorporating amortised experimental design into IRT. Here, the computational cost is shifted to a precomputing phase by training a Deep Reinforcement Learning (DRL) agent with synthetic data. The agent is trained to select optimally informative test items for the distribution of students, and to conduct amortised inference conditioned on the experiment outcomes. During deployment the agent estimates parameters from data, and suggests the next test item for the student, in close to real-time, by taking into account the history of experiments and outcomes.

Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the necessity of modeling time-varying discounting in certain applications. This paper studies a model of infinite-horizon MDPs with time-varying discount factors. We take a game-theoretic perspective -- whereby each time step is treated as an independent decision maker with their own (fixed) discount factor -- and we study the subgame perfect equilibrium (SPE) of the resulting game as well as the related algorithmic problems. We present a constructive proof of the existence of an SPE and demonstrate the EXPTIME-hardness of computing an SPE. We also turn to the approximate notion of $\epsilon$-SPE and show that an $\epsilon$-SPE exists under milder assumptions. An algorithm is presented to compute an $\epsilon$-SPE, of which an upper bound of the time complexity, as a function of the convergence property of the time-varying discount factor, is provided.

Traffic simulation software is used by transportation researchers and engineers to design and evaluate changes to roadways. These simulators are driven by models of microscopic driver behavior from which macroscopic measures like flow and congestion can be derived. Many models are designed for a subset of possible traffic scenarios and roadway configurations, while others have no explicit constraints on their application. Work zones (WZs) are one scenario for which no model to date has reproduced realistic driving behavior. This makes it difficult to optimize for safety and other metrics when designing a WZ. The Federal Highway Administration commissioned the USDOT Volpe Center to develop a car-following (CF) model for use in microscopic simulators that can capture and reproduce driver behavior accurately within and outside of WZs. Volpe also performed a naturalistic driving study to collect telematics data from vehicles driven on roads with WZs for use in model calibration. During model development, Volpe researchers observed difficulties in calibrating their model, leaving them to question whether there existed flaws in their model, in the data, or in the procedure used to calibrate the model using the data. In this thesis, I use Bayesian methods for data analysis and parameter estimation to explore and, where possible, address these questions. First, I use Bayesian inference to measure the sufficiency of the size of the data set. Second, I compare the procedure and results of the genetic algorithm based calibration performed by the Volpe researchers with those of Bayesian calibration. Third, I explore the benefits of modeling CF hierarchically. Finally, I apply what was learned in the first three phases using an established CF model, Wiedemann 99, to the probabilistic modeling of the Volpe model. Validation is performed using information criteria as an estimate of predictive accuracy.