Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences. However, when only short sequences are available, the lack of data amplifies the risk of overfitting and regularization becomes critical. Due to the challenges of hyper-parameter tuning, state-of-the-art methods only parameterize regularizers by a single shared hyper-parameter, hence limiting the power of representation of the model. To solve both issues, we develop in this work an efficient algorithm based on variational expectation-maximization.

We study algorithms using randomized value functions for exploration in reinforcement learning. This type of algorithms enjoys appealing empirical performance. We show that when we use 1) a single random seed in each episode, and 2) a Bernstein-type magnitude of noise, we obtain a worst-case \widetilde{O}\left(H\sqrt{SAT}\right) regret bound for episodic time-inhomogeneous Markov Decision Process where S is the size of state space, A is the size of action space, H is the planning horizon and T is the number of interactions. This bound polynomially improves all existing bounds for algorithms based on randomized value functions, and for the first time, matches the \Omega\left(H\sqrt{SAT}\right) lower bound up to logarithmic factors. Our result highlights that randomized exploration can be near-optimal, which was previously achieved only by optimistic algorithms.

This work tackles the problem of robust zero-shot planning in non-stationary stochastic environments. We study Markov Decision Processes (MDPs) evolving over time and consider Model-Based Reinforcement Learning algorithms in this setting. We make two hypotheses: 1) the environment evolves continuously with a bounded evolution rate; 2) a current model is known at each decision epoch but not its evolution. Our contribution can be presented in four points. We introduce the notion of regular evolution by making an hypothesis of Lipschitz-Continuity on the transition and reward functions w.r.t.

We study the problem of learning the transition matrices of a set of Markov chains from a single stream of observations on each chain. We assume that the Markov chains are ergodic but otherwise unknown. The learner can sample Markov chains sequentially to observe their states. The goal of the learner is to sequentially select various chains to learn transition matrices uniformly well with respect to some loss function. We introduce a notion of loss that naturally extends the squared loss for learning distributions to the case of Markov chains, and further characterize the notion of being \emph{uniformly good} in all problem instances.

We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the existing methods are either computationally impractical when dealing with large graphs or lacking completeness guarantees. We propose a novel computationally efficient recursive constraint-based method that is sound and complete. The key idea of our approach is that at each iteration a specific type of variable is identified and removed. This allows us to learn the structure efficiently and recursively, as this technique reduces both the number of required conditional independence (CI) tests and the size of the conditioning sets.

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the geometry of the resulting posterior distribution and can be prohibitively slow. An alternative is to use a Laplace approximation to marginalize out the latent Gaussian variables and then integrate out the remaining hyperparameters using dynamic Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo sampler. To implement this scheme efficiently, we derive a novel adjoint method that propagates the minimal information needed to construct the gradient of the approximate marginal likelihood. This strategy yields a scalable differentiation method that is orders of magnitude faster than state of the art differentiation techniques when the hyperparameters are high dimensional.

We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and then iteratively refines estimates both on graph clustering and matrix ratings. Under a hierarchical stochastic block model that well respects practically-relevant social graphs and a low-rank rating matrix model (to be detailed), we demonstrate that our algorithm achieves the information-theoretic limit on the number of observed matrix entries (i.e., optimal sample complexity) that is derived by maximum likelihood estimation together with a lower-bound impossibility result. One consequence of this result is that exploiting the hierarchical structure of social graphs yields a substantial gain in sample complexity relative to the one that simply identifies different groups without resorting to the relational structure across them. We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information.

The 2024 Nobel Prizes for physics and chemistry were announced on 8 and 9 October respectively. Both prizes were awarded for work enabling or using machine learning. More specifically, Hopfield is recognised for "inventing a network that uses a method for saving and recreating patterns". This Hopfield network utilises physics that describes a material's characteristics due to its atomic spin. The network as a whole is described in a manner equivalent to the energy in the spin system found in physics, and is trained by finding values for the connections between the nodes so that the saved images have low energy.

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be unfeasible. We propose a new class of methods to overcome these challenges in the common case of sparse constraints, where one has a large number of constraints and each only involves a few elements. Our methods rely on a basis transformation into blocks of constrained versus non-constrained subspaces, and we show that the methods greatly outperform existing alternatives in terms of computational cost. By combining the proposed methods with the stochastic partial differential equation approach for Gaussian random fields, we also show how to formulate Gaussian process regression with linear constraints in a GMRF setting to reduce computational cost.

This paper proposes a partitioning structure learning method for segmented linear regression trees (SLRT), which assigns linear predictors over the terminal nodes. The recursive partitioning process is driven by an adaptive split selection algorithm that maximizes, at each node, a criterion function based on a conditional Kendall's τ statistic that measures the rank dependence between the regressors and the fit- ted linear residuals. Theoretical analysis shows that the split selection algorithm permits consistent identification and estimation of the unknown segments. A suffi- ciently large tree is induced by applying the split selection algorithm recursively. Then the minimal cost-complexity tree pruning procedure is applied to attain the right-sized tree, that ensures (i) the nested structure of pruned subtrees and (ii) consistent estimation to the number of segments.