Neural networks (NN) have become almost ubiquitous with image classification, but in their standard form produce point estimates, with no measure of confidence. Bayesian neural networks (BNN) provide uncertainty quantification (UQ) for NN predictions and estimates through the posterior distribution. As NN are applied in more high-consequence applications, UQ is becoming a requirement. BNN provide a solution to this problem by not only giving accurate predictions and estimates, but also an interval that includes reasonable values within a desired probability. Despite their positive attributes, BNN are notoriously difficult and time consuming to train. Traditional Bayesian methods use Markov Chain Monte Carlo (MCMC), but this is often brushed aside as being too slow. The most common method is variational inference (VI) due to its fast computation, but there are multiple concerns with its efficacy. We apply and compare MCMC- and VI-trained BNN in the context of target detection in hyperspectral imagery (HSI), where materials of interest can be identified by their unique spectral signature. This is a challenging field, due to the numerous permuting effects practical collection of HSI has on measured spectra. Both models are trained using out-of-the-box tools on a high fidelity HSI target detection scene. Both MCMC- and VI-trained BNN perform well overall at target detection on a simulated HSI scene. This paper provides an example of how to utilize the benefits of UQ, but also to increase awareness that different training methods can give different results for the same model. If sufficient computational resources are available, the best approach rather than the fastest or most efficient should be used, especially for high consequence problems.

The evolutionary distance between two species is proportional to some (unknown) function of the time of divergence from their common ancestor. One way to estimate this time is by comparing the underlying macromolecular sequences that cascade the information of accumulated evolutionary changes across DNA RNA Proteins (sequence structure function). Since the introduction of the molecular evolutionary clock by Zuckerkandl and Pauling (1965) to perform phylogenetic studies, several statistical models have been proposed to estimate the divergence of extant sequences from common ancestors, and to correlate the estimates of time from other sources of information (e.g., fossil records) when they exist (Sarich and Wilson, 1967). Such divergence time estimates require reliable statistical models of DNA/RNA/Proteins macromolecules (Bromham and Penny, 2003). For protein amino acid sequences, several statistical models have been proposed to explain sequence variation as a function of time. The point accepted mutation (PAM) matrix of Dayhoff et al. (1978) was the first successful model to explain the mutability of amino acid sequences. PAM is a stochastic (Markov) matrix defined in PAM (time) units where PAM-1 is a Markov matrix that embodies a 1% expected change to the amino acids. Subsequent studies highlighted the importance of incorporating evolutionary time-dependent substitution and gap models as an elegant way to model the divergent relationships of proteins (Holmes, 1998; Gonnet et al., 1992). The recent approach of Sumanaweera et al. (2022) derives a unified statistical model for quantifying the evolution of pairs of protein sequences

Traditional deep learning (DL) models are powerful classifiers, but many approaches do not provide uncertainties for their estimates. Uncertainty quantification (UQ) methods for DL models have received increased attention in the literature due to their usefulness in decision making, particularly for high-consequence decisions. However, there has been little research done on how to evaluate the quality of such methods. We use statistical methods of frequentist interval coverage and interval width to evaluate the quality of credible intervals, and expected calibration error to evaluate classification predicted confidence. These metrics are evaluated on Bayesian neural networks (BNN) fit using Markov Chain Monte Carlo (MCMC) and variational inference (VI), bootstrapped neural networks (NN), Deep Ensembles (DE), and Monte Carlo (MC) dropout. We apply these different UQ for DL methods to a hyperspectral image target detection problem and show the inconsistency of the different methods' results and the necessity of a UQ quality metric. To reconcile these differences and choose a UQ method that appropriately quantifies the uncertainty, we create a simulated data set with fully parameterized probability distribution for a two-class classification problem. The gold standard MCMC performs the best overall, and the bootstrapped NN is a close second, requiring the same computational expense as DE. Through this comparison, we demonstrate that, for a given data set, different models can produce uncertainty estimates of markedly different quality. This in turn points to a great need for principled assessment methods of UQ quality in DL applications.

Human-Robot Interaction (HRI) becomes more and more important in a world where robots integrate fast in all aspects of our lives but HRI applications depend massively on the utilized robotic system as well as the deployment environment and cultural differences. Because of these variable dependencies it is often not feasible to use a data-driven approach to train a model for human intent recognition. Expert systems have been proven to close this gap very efficiently. Furthermore, it is important to support understandability in HRI systems to establish trust in the system. To address the above-mentioned challenges in HRI we present an adaptable python library in which current state-of-the-art Models for context recognition can be integrated. For Context-Based Intention Recognition a two-layer Bayesian Network (BN) is used. The bayesian approach offers explainability and clarity in the creation of scenarios and is easily extendable with more modalities. Additionally, it can be used as an expert system if no data is available but can as well be fine-tuned when data becomes available.

Spike trains data find a growing list of applications in computational neuroscience, imaging, streaming data and finance. Machine learning strategies for spike trains are based on various neural network and probabilistic models. The probabilistic approach is relying on parametric or nonparametric specifications of the underlying spike generation model. In this paper we consider the two-class statistical classification problem for a class of spike train data characterized by nonparametrically specified intensity functions. We derive the optimal Bayes rule and next form the plug-in nonparametric kernel classifier. Asymptotical properties of the rules are established including the limit with respect to the increasing recording time interval and the size of a training set. In particular the convergence of the kernel classifier to the Bayes rule is proved. The obtained results are supported by a finite sample simulation studies.

We consider the problem of time-limited robotic exploration in previously unseen environments where exploration is limited by a predefined amount of time. We propose a novel exploration approach using learning-augmented model-based planning. We generate a set of subgoals associated with frontiers on the current map and derive a Bellman Equation for exploration with these subgoals. Visual sensing and advances in semantic mapping of indoor scenes are exploited for training a deep convolutional neural network to estimate properties associated with each frontier: the expected unobserved area beyond the frontier and the expected timesteps (discretized actions) required to explore it. The proposed model-based planner is guaranteed to explore the whole scene if time permits. We thoroughly evaluate our approach on a large-scale pseudo-realistic indoor dataset (Matterport3D) with the Habitat simulator. We compare our approach with classical and more recent RL-based exploration methods. Our approach surpasses the greedy strategies by 2.1% and the RL-based exploration methods by 8.4% in terms of coverage.

Multi-task learning is frequently used to model a set of related response variables from the same set of features, improving predictive performance and modeling accuracy relative to methods that handle each response variable separately. Despite the potential of multi-task learning to yield more powerful inference than single-task alternatives, prior work in this area has largely omitted uncertainty quantification. Our focus in this paper is a common multi-task problem in neuroimaging, where the goal is to understand the relationship between multiple cognitive task scores (or other subject-level assessments) and brain connectome data collected from imaging. We propose a framework for selective inference to address this problem, with the flexibility to: (i) jointly identify the relevant covariates for each task through a sparsity-inducing penalty, and (ii) conduct valid inference in a model based on the estimated sparsity structure. Our framework offers a new conditional procedure for inference, based on a refinement of the selection event that yields a tractable selection-adjusted likelihood. This gives an approximate system of estimating equations for maximum likelihood inference, solvable via a single convex optimization problem, and enables us to efficiently form confidence intervals with approximately the correct coverage. Applied to both simulated data and data from the Adolescent Brain Cognitive Development (ABCD) study, our selective inference methods yield tighter confidence intervals than commonly used alternatives, such as data splitting. We also demonstrate through simulations that multi-task learning with selective inference can more accurately recover true signals than single-task methods.

Thesis concerns the study and development of hierarchical representations for spatio-temporal visual attention modeling and understanding in video sequences. More specifically, we propose two computational models for visual attention. First, we present a generative probabilistic model for context-aware visual attention modeling and understanding. Secondly, we develop a deep network architecture for visual attention modeling, which first estimates top-down spatio-temporal visual attention, and ultimately serves for modeling attention in the temporal domain. The first part of the thesis introduces our first proposal: a generative probabilistic framework for spatio-temporal visual attention modeling and understanding.

We present a novel computational model employing hierarchical active inference to simulate reading and eye movements. The model characterizes linguistic processing as inference over a hierarchical generative model, facilitating predictions and inferences at various levels of granularity, from syllables to sentences. Our approach combines the strengths of large language models for realistic textual predictions and active inference for guiding eye movements to informative textual information, enabling the testing of predictions. The model exhibits proficiency in reading both known and unknown words and sentences, adhering to the distinction between lexical and nonlexical routes in dual-route theories of reading. Notably, our model permits the exploration of maladaptive inference effects on eye movements during reading, such as in dyslexia. To simulate this condition, we attenuate the contribution of priors during the reading process, leading to incorrect inferences and a more fragmented reading style, characterized by a greater number of shorter saccades. This alignment with empirical findings regarding eye movements in dyslexic individuals highlights the model's potential to aid in understanding the cognitive processes underlying reading and eye movements, as well as how reading deficits associated with dyslexia may emerge from maladaptive predictive processing. In summary, our model represents a significant advancement in comprehending the intricate cognitive processes involved in reading and eye movements, with potential implications for understanding and addressing dyslexia through the simulation of maladaptive inference. It may offer valuable insights into this condition and contribute to the development of more effective interventions for treatment.

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.