We study the Bayesian regret of the renowned Thompson Sampling algorithm in contextual bandits with binary losses and adversarially-selected contexts.

We study pointwise estimation and uncertainty quantification for a sparse varia-tional Gaussian process method with eigenvector inducing variables.

Personalised federated learning (FL) aims at collaboratively learning a machine learning model tailored for each client.

Gaussian processes are important models in the field of probabilistic numerics. We present a procedure for optimizing Mat ern kernel temporal Gaussian processes with respect to the kernel covariance function's hyperparameters. It is based on casting the optimization problem as a recursive Bayesian estimation procedure for the parameters of an autoregressive model. We demonstrate that the proposed procedure outperforms maximizing the marginal likelihood as well as Hamiltonian Monte Carlo sampling, both in terms of runtime and ultimate root mean square error in Gaussian process regression.

Road traffic congestion is a persistent problem. Focusing resources on the causes of congestion is a potentially efficient strategy for reducing slowdowns. We present NEXICA, an algorithm to discover which parts of the highway system tend to cause slowdowns on other parts of the highway. We use time series of road speeds as inputs to our causal discovery algorithm. Finding other algorithms inadequate, we develop a new approach that is novel in three ways. First, it concentrates on just the presence or absence of events in the time series, where an event indicates the temporal beginning of a traffic slowdown. Second, we develop a probabilistic model using maximum likelihood estimation to compute the probabilities of spontaneous and caused slowdowns between two locations on the highway. Third, we train a binary classifier to identify pairs of cause/effect locations trained on pairs of road locations where we are reasonably certain a priori of their causal connections, both positive and negative. We test our approach on six months of road speed data from 195 different highway speed sensors in the Los Angeles area, showing that our approach is superior to state-of-the-art baselines in both accuracy and computation speed.

Backpropagation (BP) of errors is the backbone training algorithm for artificial neural networks (ANNs). It updates network weights through gradient descent to minimize a loss function representing the mismatch between predictions and desired outputs. BP uses the chain rule to propagate the loss gradient backward through the network hierarchy, allowing efficient weight updates. However, this process requires weight updates at every layer to rely on a global error signal generated at the network's output. In contrast, the Hebbian model of synaptic plasticity states that weight updates are local, depending only on the activity of pre- and post-synaptic neurons. This suggests biological brains likely do not implement BP directly. Recently, Predictive Coding (PC) has gained interest as a biologically plausible alternative that updates weights using only local information. Originating from 1950s work on signal compression, PC was later proposed as a model of the visual cortex and formalized under the free energy principle, linking it to Bayesian inference and dynamical systems. PC weight updates rely solely on local information and provide theoretical advantages such as automatic scaling of gradients based on uncertainty. This lecture notes column offers a novel, tutorial-style introduction to PC, focusing on its formulation, derivation, and connections to well-known optimization and signal processing algorithms such as BP and the Kalman Filter (KF). It aims to support existing literature by guiding readers from the mathematical foundations of PC to practical implementation, including Python examples using PyTorch.

The scientific process is a means for turning the results of experiments into knowledge about the world in which we live. Much research effort has been directed toward automating this process. To do this, one needs to formulate the scientific process in a precise mathematical language. This paper outlines one such language. What is presented here is hardly new. The material leans much on great thinkers of times past as well as more modern contributions. The novel contributions of this paper are: A new, general data processing inequality, a bias variance decomposition for canonical losses, Streamlined proofs of the Blackwell-Sherman-Stein and Randomization Theorems, and Means to calculate deficiency via linear programming.

Understanding causal relationships between variables is fundamental across scientific disciplines. Most causal discovery algorithms rely on two key assumptions: (i) all variables are observed, and (ii) the underlying causal graph is acyclic. While these assumptions simplify theoretical analysis, they are often violated in real-world systems, such as biological networks. Existing methods that account for confounders either assume linearity or struggle with scalability. To address these limitations, we propose DCCD-CONF, a novel framework for differentiable learning of nonlinear cyclic causal graphs in the presence of unmeasured confounders using interventional data. Our approach alternates between optimizing the graph structure and estimating the confounder distribution by maximizing the log-likelihood of the data. Through experiments on synthetic data and real-world gene perturbation datasets, we show that DCCD-CONF outperforms state-of-the-art methods in both causal graph recovery and confounder identification. Additionally, we also provide consistency guarantees for our framework, reinforcing its theoretical soundness.