Continual learning aims to learn new tasks without forgetting previously learned ones. This is especially challenging when one cannot access data from previous tasks and when the model has a fixed capacity. Current regularization-based continual learning algorithms need an external representation and extra computation to measure the parameters' importance. In contrast, we propose Uncertainty-guided Continual Bayesian Neural Networks (UCB), where the learning rate adapts according to the uncertainty defined in the probability distribution of the weights in networks. Uncertainty is a natural way to identify what to remember and what to change as we continually learn, allowing to mitigate catastrophic forgetting. We also show a variant of our model, which uses uncertainty for weight pruning and retains task performance after pruning by saving binary masks per tasks. We evaluate our UCB approach extensively on diverse object classification datasets with short and long sequences of tasks and report superior or on-par performance compared to existing approaches. Additionally, we show that our model does not necessarily need task information at test time, i.e. it does not presume knowledge of which task a sample belongs to.

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is optimization based. Concepts such as regularization will be utilized for encoding of prior knowledge and basis-function expansions will be used to add nonlinear modeling power while keeping data requirements practical. The thesis covers a wide range of applications, many inspired by applications within robotics, but also extending outside this already wide field. Usage of the proposed methods and algorithms are in many cases illustrated in the real-world applications that motivated the research. Topics covered include dynamics modeling and estimation, model-based reinforcement learning, spectral estimation, friction modeling and state estimation and calibration in robotic machining. In the work on modeling and identification of dynamics, we develop regularization strategies that allow us to incorporate prior domain knowledge into flexible, overparameterized models. We make use of classical control theory to gain insight into training and regularization while using flexible tools from modern deep learning. A particular focus of the work is to allow use of modern methods in scenarios where gathering data is associated with a high cost. In the robotics-inspired parts of the thesis, we develop methods that are practically motivated and ensure that they are implementable also outside the research setting. We demonstrate this by performing experiments in realistic settings and providing open-source implementations of all proposed methods and algorithms.

This paper focuses on the problem of hierarchical non-overlapping clustering of a dataset. In such a clustering, each data item is associated with exactly one leaf node and each internal node is associated with all the data items stored in the sub-tree beneath it, so that each level of the hierarchy corresponds to a partition of the dataset. We develop a novel Bayesian nonparametric method combining the nested Chinese Restaurant Process (nCRP) and the Hierarchical Dirichlet Process (HDP). Compared with other existing Bayesian approaches, our solution tackles data with complex latent mixture features which has not been previously explored in the literature. We discuss the details of the model and the inference procedure. Furthermore, experiments on three datasets show that our method achieves solid empirical results in comparison with existing algorithms.

The idea of Artificial Intelligence (AI) has a long history. It turned out, however, that reaching intelligence at human levels is more complicated than originally anticipated. Currently we are experiencing a renewed interest in AI, fueled by an enormous increase in computing power and an even larger increase in data, in combination with improved AI technologies like deep learning. Healthcare is considered the next domain to be revolutionized by Artificial Intelligence. While AI approaches are excellently suited to develop certain algorithms, for biomedical applications there are specific challenges. We propose recommendations to improve AI projects in the biomedical space and especially clinical healthcare.

We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables using neural networks. This extension allows to model complex interactions while being more global in its search compared to other greedy approaches. In addition to comparing our method to existing continuous optimization methods, we provide missing empirical comparisons to nonlinear greedy search methods. On both synthetic and real-world data sets, this new method outperforms current continuous methods on most tasks while being competitive with existing greedy search methods on important metrics for causal inference.

We posit that hippocampal place cells encode information about future locations under a transition distribution observed as an agent explores a given (physical or conceptual) space. The encoding of information about the current location, usually associated with place cells, then emerges as a necessary step to achieve this broader goal. We formally derive a biologically-inspired neural network from Nystr\"om kernel approximations and empirically demonstrate that the network successfully approximates transition distributions. The proposed network yields representations that, just like place cells, soft-tile the input space with highly sparse and localized receptive fields. Additionally, we show that the proposed computational motif can be extended to handle supervised problems, creating class-specific place cells while exhibiting low sample complexity.

We consider optimization of composite objective functions, i.e., of the form $f(x)=g(h(x))$, where $h$ is a black-box derivative-free expensive-to-evaluate function with vector-valued outputs, and $g$ is a cheap-to-evaluate real-valued function. While these problems can be solved with standard Bayesian optimization, we propose a novel approach that exploits the composite structure of the objective function to substantially improve sampling efficiency. Our approach models $h$ using a multi-output Gaussian process and chooses where to sample using the expected improvement evaluated on the implied non-Gaussian posterior on $f$, which we call expected improvement for composite functions (\ei). Although \ei\ cannot be computed in closed form, we provide a novel stochastic gradient estimator that allows its efficient maximization. We also show that our approach is asymptotically consistent, i.e., that it recovers a globally optimal solution as sampling effort grows to infinity, generalizing previous convergence results for classical expected improvement. Numerical experiments show that our approach dramatically outperforms standard Bayesian optimization benchmarks, reducing simple regret by several orders of magnitude.

We study pool-based active learning with abstention feedbacks where a labeler can abstain from labeling a queried example with some unknown abstention rate. Using the Bayesian approach, we develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by incorporating the estimated average abstention rate into the greedy criteria. We prove that both algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or worst-case value of a useful utility function. Our experiments show the algorithms perform well in various practical scenarios.

Chart-based visual acuity measurements are used by billions of people to diagnose and guide treatment of vision impairment. However, the ubiquitous eye exam has no mechanism for reasoning about uncertainty and as such, suffers from a well-documented reproducibility problem. In this paper we uncover a new parametric probabilistic model of visual acuity response based on measurements of patients with eye disease. We present a state of the art eye exam which (1) reduces acuity exam error by 75\% without increasing exam length, (2) knows how confident it should be, (3) can trace predictions over time and incorporate prior beliefs and (4) provides insight for educational Item Response Theory. For patients with more serious eye disease, the novel ability to finely measure acuity from home could be a crucial part in early diagnosis. We provide a web implementation of our algorithm for anyone in the world to use.

We propose and investigate new complementary methodologies for estimating predictive variance networks in regression neural networks. We derive a locally aware mini-batching scheme that result in sparse robust gradients, and show how to make unbiased weight updates to a variance network. Further, we formulate a heuristic for robustly fitting both the mean and variance networks post hoc. Finally, we take inspiration from posterior Gaussian processes and propose a network architecture with similar extrapolation properties to Gaussian processes. The proposed methodologies are complementary, and improve upon baseline methods individually. Experimentally, we investigate the impact on predictive uncertainty on multiple datasets and tasks ranging from regression, active learning and generative modeling. Experiments consistently show significant improvements in predictive uncertainty estimation over state-of-the-art methods across tasks and datasets.