As an important semi-supervised learning task, positive-unlabeled (PU) learning aims to learn a binary classifier only from positive and unlabeled data. In this article, we develop a novel PU learning framework, called discriminative adversarial networks, which contains two discriminative models represented by deep neural networks. One model $\Phi$ predicts the conditional probability of the positive label for a given sample, which defines a Bayes classifier after training, and the other model $D$ distinguishes labeled positive data from those identified by $\Phi$. The two models are simultaneously trained in an adversarial way like generative adversarial networks, and the equilibrium can be achieved when the output of $\Phi$ is close to the exact posterior probability of the positive class. In contrast with existing deep PU learning approaches, DAN does not require the class prior estimation, and its consistency can be proved under very general conditions. Numerical experiments demonstrate the effectiveness of the proposed framework.

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.

Deep neural networks (DNN) and Gaussian processes (GP) are two powerful models with several theoretical connections relating them, but the relationship between their training methods is not well understood. In this paper, we show that certain Gaussian posterior approximations for Bayesian DNNs are equivalent to GP posteriors. As a result, we can obtain a GP kernel and a nonlinear feature map simply by training the DNN. Surprisingly, the resulting kernel is the neural tangent kernel which has desirable theoretical properties for infinitely-wide DNNs. We show feature maps obtained on real datasets and demonstrate the use of the GP marginal likelihood to tune hyperparameters of DNNs. Our work aims to facilitate further research on combining DNNs and GPs in practical settings.

The creation and performance of music has inspired AI researchers since the very early times of artificial intelligence [8, 13, 10], and there is today a rich literature of computational approaches to music [11], including AI systems for music composition [3] and improvisation [2]. As pointed out by Thom [15], however, these systems rarely focus on the spontanous interaction between the human and the artificial musicians. We claim that such interaction demands a combination of reactivity and anticipation, that is, the ability to act now based on a predictive model of the companion player [12]. This paper reports our initial steps in the generation of collaborative human-machine music performance, as a special case of the more general problem of anticipation and creative processes in mixed human-robot, or anthrobotic systems [4]. We consider a simple case study of a duo consisting of a human pianist accompained by an off-the-shelf virtual drummer, and we design an AI system to control the key perfomance parameters of the virtual drummer (patterns, intensity, complexity, fills, and so on) as a function of what the human pianist is playing. The AI system is knowledge-based: it relies on an internal model represented by means of fuzzy logic.

Brain source imaging is an important method for noninvasively characterizing brain activity using Electroencephalogram (EEG) or Magnetoencephalography (MEG) recordings. Traditional EEG/MEG Source Imaging (ESI) methods usually assume that either source activity at different time points is unrelated, or that similar spatiotemporal patterns exist across an entire study period. The former assumption makes ESI analyses sensitive to noise, while the latter renders ESI analyses unable to account for time-varying patterns of activity. To effectively deal with noise while maintaining flexibility and continuity among brain activation patterns, we propose a novel probabilistic ESI model based on a hierarchical graph prior. Under our method, a spanning tree constraint ensures that activity patterns have spatiotemporal continuity. An efficient algorithm based on alternating convex search is presented to solve the proposed model and is provably convergent. Comprehensive numerical studies using synthetic data on a real brain model are conducted under different levels of signal-to-noise ratio (SNR) from both sensor and source spaces. We also examine the EEG/MEG data in a real application, in which our ESI reconstructions are neurologically plausible. All the results demonstrate significant improvements of the proposed algorithm over the benchmark methods in terms of source localization performance, especially at high noise levels.

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 Bayesian approach to spectral graph convolutional networks (GCNs) where the graph parameters are considered as random variables. We develop an inference algorithm to estimate the posterior over these parameters and use it to incorporate prior information that is not naturally considered by standard GCN. The key to our approach is to define a smooth posterior parameterization over the adjacency matrix characterizing the graph, which we estimate via stochastic variational inference. Our experiments show that we can outperform standard GCN methods in the task of semi-supervised classification in noisy-graph regimes.

Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-series analysis. While k-nearest neighbor (kNN) based estimators as well as kernel-based methods have been widely used for CMI estimation, they suffer severely from the curse of dimensionality. In this paper, we leverage advances in classifiers and generative models to design methods for CMI estimation. Specifically, we introduce an estimator for KL-Divergence based on the likelihood ratio by training a classifier to distinguish the observed joint distribution from the product distribution. We then show how to construct several CMI estimators using this basic divergence estimator by drawing ideas from conditional generative models. We demonstrate that the estimates from our proposed approaches do not degrade in performance with increasing dimension and obtain significant improvement over the widely used KSG estimator. Finally, as an application of accurate CMI estimation, we use our best estimator for conditional independence testing and achieve superior performance than the state-of-the-art tester on both simulated and real data-sets.

Fast covariance calculation is required both for SLAM (e.g.~in order to solve data association) and for evaluating the information-theoretic term for different candidate actions in belief space planning (BSP). In this paper we make two primary contributions. First, we develop a novel general-purpose incremental covariance update technique, which efficiently recovers specific covariance entries after any change in the inference problem, such as introduction of new observations/variables or re-linearization of the state vector. Our approach is shown to recover them faster than other state-of-the-art methods. Second, we present a computationally efficient approach for BSP in high-dimensional state spaces, leveraging our incremental covariance update method. State of the art BSP approaches perform belief propagation for each candidate action and then evaluate an objective function that typically includes an information-theoretic term, such as entropy or information gain. Yet, candidate actions often have similar parts (e.g. common trajectory parts), which are however evaluated separately for each candidate. Moreover, calculating the information-theoretic term involves a costly determinant computation of the entire information (covariance) matrix which is O(n^3) with n being dimension of the state or costly Schur complement operations if only marginal posterior covariance of certain variables is of interest. Our approach, rAMDL-Tree, extends our previous BSP method rAMDL, by exploiting incremental covariance calculation and performing calculation re-use between common parts of non-myopic candidate actions, such that these parts are evaluated only once, in contrast to existing approaches.