Learning Graphical Models
Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential families
In practice, however, they are very efficient.
Online Variational Filtering and Parameter Learning
As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states' posterior distribution.
In Appendix A we provide heuristic justification for the scaling of the optimal error rate
In Appendix D we provide the proofs for Theorem 7. In Appendix E we include some useful results for the sake of completeness. Informally, we expect that there is one sign flip (i.e., The top left, top right and bottom left figures show the scaling of the minimax rates of GLM (cf. To begin with the analysis of the estimator in Figure 2, the following lemma is a simple, yet key tool for the proof. It establishes the variance of the random gain S . The proof relies on a sort of self-bounding property (cf.
Mean Estimation in High-Dimensional Binary Markov Gaussian Mixture Models
It was also extensively studied from the theoretical perspective in the classical, fixed-dimensional and asymptotic regime, e.g., Györfi et al. [2002, Chapter 27 and
PAC-Bayes Analysis Beyond the Usual Bounds
We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution is then used to make randomized predictions, and the high-level theme addressed here is guaranteeing the quality of predictions on examples that were not seen during training, i.e. generalization. In this setting the unknown quantity of interest is the expected risk of the data-dependent randomized predictor, for which upper bounds can be derived via a P AC-Bayes analysis, leading to P AC-Bayes bounds. Specifically, we present a basic P AC-Bayes inequality for stochastic kernels, from which one may derive extensions of various known P AC-Bayes bounds as well as novel bounds. We clarify the role of the requirements of fixed'data-free' priors, bounded losses, and i.i.d.
Bayesian Clustering of Neural Spiking Activity Using a Mixture of Dynamic Poisson Factor Analyzers
With modern high-density probes (Jun et al., 2017), neuroscientists can observe the spiking activity
Simultaneously Learning Stochastic and Adversarial Episodic MDPs with Known Transition
We study the problem of learning episodic Markov Decision Processes (MDPs).