Dario Gasbarra (University of Vaasa)
Title: TBA
Abstract: TBA
Jukka Lempa (University of Turku) (Talk on Friday)
Title: Learning in optimal stopping and control
Abstract: The purpose of this talk is to discuss some recent developments in applications of learning in optimal stopping and control problems.
Lasse Leskelä (Aalto University, Espoo)
Title: Consistent spectral clustering in sparse tensor block models
Abstract: High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, social network analysis, and recommendation systems. These tasks often involve data that is sparse and high-dimensional, presenting significant statistical and computational challenges. This paper introduces a tensor block model specifically designed for sparse integer-valued data tensors. We propose a simple spectral clustering algorithm augmented with a trimming step to mitigate noise fluctuations, and identify a density threshold that ensures the algorithm's consistency. Our approach models sparsity using a sub-Poisson noise concentration framework, accommodating heavier than sub-Gaussian tails. Remarkably, this natural class of tensor block models is closed under aggregation across arbitrary modes. Consequently, we obtain a comprehensive framework for evaluating the tradeoff between signal loss and noise reduction during data aggregation. The analysis is based on a novel concentration bound for sparse random Gram matrices. The theoretical findings are illustrated through simulation experiments. The talk is based on joint work with Ian Välimaa (https://arxiv.org/abs/2501.13820).
Greta Panova (University of Southern California, USA) (Talk on Thursday)
Title: Algebra meets probability: permutons from pipe dreams via Aztec diamonds and TASEP
Abstract: Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian in algebraic geometry and are parametrized by permutations. They can also be viewed as ensembles of random lattice walks with various interaction constraints. In one case these are long-range interactions and still beyond reach, but in the other case a striking connection with the Aztec diamond allows us to determine when maxima occur. We also study the typical permutation arising from the measure and determine the arising permutons via a different connection with the theory of the Totally Asymmetric Simple Exclusion Process (TASEP).
This is based on joint work with A. H. Morales, L. Petrov, D. Yeliussizov.
Ellen Powell (Durham University, UK)
Title: Scaling limits of critical FK-decorated maps at q=4.
Abstract: The critical Fortuin–Kasteleyn random planar map with parameter q>0 is a model of random (discretised) surfaces decorated by loops, related to the q-state Potts model. For q<4, Sheffield established a scaling limit result for these discretised surfaces, where the limit is described by a so-called Liouville quantum gravity surface decorated by a conformal loop ensemble. At q=4 a phase transition occurs, and the correct rescaling needed to obtain a limit has so far remained unclear. I will talk about joint work with William Da Silva, XinJiang Hu, and Mo Dick Wong, where we identify the right rescaling at this critical value and prove a number of convergence results.
Eero Saksman (University of Helsinki)
Title: Chaos and Riemann zeta function on the critical line
Abstract: We will discuss some results, both old and new, on the statistics of the Riemann zeta function on short intervals on the critical line. The talk is based on collaboration with Adam Harper (Warwick) and Christian Webb (Helsinki).
Etienne Sebag (University of Helsinki) (Talk on Thursday)
Title: Non-homogeneous multistate models for intermittently observed
Processes.
Abstract: Multistate models are useful to capture jump-based behavior within a discrete state space, and examples include biological life processes where an individual moves from one health state to another. Often, the underlying dynamic process is a time non-homogeneous Markov process. When dealing with panel data, the exact transition time is never directly observed, which is known as an interval-censoring mechanism. The transition probabilities are therefore used to formulate a likelihood function due to the intermittent observations of the process. Frequently, the underlying computations do not have a nice closed form analytical expression when the transition rates are time-dependent. Additionally, when the time grids are highly irregular, or sparse, then current statistical software packages to analyze non-homogeneous Markov multistate models are limited and often fail. We therefore propose an honest time data augmentation algorithm which eliminates the need altogether to use intractable computations in two-state models. Our method also provides unbiased estimates of the transition probabilities.
Matti Vihola (University of Jyväskylä)
Title: On the forgetting of particle filters
Abstract: We study the forgetting properties of the particle filter algorithm when its state - the collection of interacting particles - is regarded as a Markov chain. Under a strong mixing assumption on the particle filter's underlying model, we find that the particle filter is exponentially mixing, and forgets its initial state in O(log N) 'time', where N is the number of particles and time refers to the number of particle filter algorithm steps, each comprising a selection (or resampling) and mutation (or prediction) operation. We present an example which shows that this rate is optimal. We also study the conditional particle filter (CPF) and extend our forgetting result to this context. We establish a similar conclusion, namely, CPF is exponentially mixing and forgets its initial state in O(log N) time - a result which was key for characterising the mixing time of the CPF. Our proof technique implies also propagation of chaos type results, which are new in the particle filter literature.