*22 November 2022, 13:00 Stockholm*

**Speaker:** Joakim Wallmark, Department of Statistics, Umeå University.

Venue: TBA

The Department of Mathematics and Mathematical Statistics and the Department of Statistics jointly organise this statistical seminar series.

*22 November 2022, 13:00 Stockholm*

**Speaker:** Joakim Wallmark, Department of Statistics, Umeå University.

Venue: TBA

*7 October 2022, 13:00 Stockholm*

**Speaker:** Niloofar Moosavi, Department of Statistics, Umeå University

Faculty opponent: Associate Professor Edward Kennedy, Carnegie Mellon University

Venue: NBET.A.101

*6 October 2022, 15:15-16:00 Stockholm*

**Speaker:** Edward Kennedy, Statistics and Data Science, Carnegie Mellon University, USA

**Abstract:** Estimation of heterogeneous causal effects – i.e., how effects of policies and treatments vary across units – is fundamental to medical, social, and other sciences, and plays a crucial role in optimal treatment allocation, generalizability, subgroup effects, and more. Many methods for estimating conditional average treatment effects (CATEs) have been proposed in recent years, but there have remained important theoretical gaps in understanding if and when such methods make optimally efficient use of the data at hand. This is especially true when the CATE has nontrivial structure (e.g., smoothness or sparsity). This talk surveys work across two recent papers in this context. First, we study a two-stage doubly robust estimator and give a generic model-free error bound, which, despite its generality, yields sharper results than those in the current literature. The second contribution is aimed at understanding the fundamental statistical limits of CATE estimation. We resolve this long-standing problem by deriving a minimax lower bound, with matching upper bound obtained via a new estimator based on higher order influence functions. Applications in medicine and political science are considered.

Venue: SAM.A.323 (S312)

*28 September 2022, 15:30 Stockholm*

**Speaker:** Axel Flinth, Umeå University

Jointly with the Seminars in Mathematical Modelling and Analysis:

**Abstract:** A key concept within the field of Geometric Deep Learning is that of equivariance. Put simply, a network is equivariant towards a group of transformations if it reacts properly to the input being transformed. A prominent example is that of convolutional neural networks: Here, a translation of the input causes the output to translate with it. In recent years, networks for a number of other transformation groups have been successfully constructed and applied. In this talk, we investigate the question of equivariance in a projective sense, and in particular the connection to equivariance in the standard sense. Our main motivation for studying projective equivariance is the pinhole camera model in computer vision, but other applications may be possible. As in many other works, we concentrate on equivariant multilayered perceptrons, and in particular linear layers. Our main theoretical finding is that in several important special cases, the problem of finding projectively equivariant linear layers is actually equivalent to the standard equivariance problem. We also present some small, proof-of-concept, numerical experiments. This talk is based on joint work with Georg Bökman and Fredrik Kahl.

Venue: MIT.A.346

27 September 2022, 13:00 - 14:00 Stockholm

**Speaker:** Hamed Sabahno, Department of Statistics, Umeå University

**Abstract: **In many practical cases, the process’s quality is characterized by the relationship between some response and independent variables in the form of a regression model (called a profile), rather than being characterized by some quality variables/attributes, i.e., the quality characteristic of the process is a regression model, not some variables/attributes. Monitoring whether this relationship (profile’s parameters) remains unchanged over time or not is called ‘profile monitoring’. It is usually assumed that the response variable in a profile follows a normal distribution. However, in many real-case applications, the response variable can be distributed non-normally and follow another type of exponential family of distributions. These models, in the case of a linear relationship (which is actually the most common one), are called generalized linear models (GLMs). The most common GLM-type distributions in profile monitoring are: Binomial, Poisson, and Gamma.

In this research, we develop three statistical based control charts: Hotelling’s T2, MEWMA (multivariate exponentially weighted moving average), and LRT (likelihood ratio test) as well as three machine learning (ML) based control charts: ANN (artificial neural network), SVR (support vector regression) and RFR (random forest regression), for monitoring GLM profiles. We train these ML techniques to get a linear (regression) output and then apply our own classification technique to see if the process is in- or out-of- control, at each sampling time. In addition to developing the FP (fixed parameter) schemes, we design an adaptive VP (variable parameters) scheme for each control chart as well to increase the charts’ sensitivity in detecting shifts, by developing some algorithms with which the values of the control chart parameters in both FP and VP schemes can be obtained. Then, we develop two Monte Carlo-based algorithms to measure the charts’ performance in both FP and VP formats, by using the run length and time to signal performance measures.

After designing the control charts as well as performance measures, which can be used for any other types of distribution-based or distribution-free control charts as well, we perform extensive simulation studies and evaluate and compare all our control charts under different shift sizes and scenarios and in three different simulation environments. At last, we present a numerical example regarding a drug dose-response study to show how the proposed control charts can be implemented in real practice.

**Keywords:** Quality Control, Variable Parameters Control Charts, Profile Monitoring, Generalized Linear Models, Machine Learning Techniques, Monte Carlo Simulation.

Venue: SAM.A.323 (S312)

*13 and 15 September 2022, 13:00 Stockholm*

Speaker: Jesper Møller, Aalborg University

**Date & Time 1:** Tues the 13th of Sep 2022; 13.00-14.00

**Venue 1:** MIT.C.323, MIT-building

**Date & Time 2:** Thur the 15th of Sep 2022; 13.00-14.00

**Venue 2:** MIT.C.413, MIT-building

**Abstract:** A point process is a mathematical model for randomly distributed point patterns in a given

space. While the mathematical and statistical theory for point processes on one, two or

higher dimensional Euclidean space is fairly well-developed with accompanying user-friendly

software for statistical analysis, notably the R package spatstat, the research on point

processes defined on more general spaces such as spheres and linear networks is in its

infancy. This talk will provide a state-of-the-art review on statistical models, simulation

procedures, and methods for estimation and model checking when analyzing point patterns

observed on spheres.

Zoom link: https://umu.zoom.us/j/67918643402

*8 September 2022, 13:00 Stockholm*

Speaker: Sahoko Ishida, London School of Economics

**Abstract:** Regression with Gaussian Process (GP) prior is a powerful statistical tool for modelling a wide variety of data with both Gaussian and non-Gaussian likelihood. In the spatial statistics community, GP regression, also known as Kriging, has a long-standing history. It has been proven useful since its introduction, due to its capability of modelling autocorrelation of spatial and spatio-temporal data.

Other than space and time, real-life applications often contain additional information with different characteristics. In applied research, interests often lie in exploring whether there exists a space-time interaction or investigating relationships with covariates and the outcome while controlling for space and time effect.

Additive GP regression allows to model such flexible relationships by exploiting the structure of the GP covariance function (kernel) by adding and multiplying different kernels for different types of covariates. This has only partially been adapted in spatial and spatio-temporal analysis.

In this study, we use ANOVA decomposition of kernels and introduce a unified approach to model spatio-temporal data, using the full flexibility of additive GP models. Not only does this permit modelling of main effects and interactions of space and time, but furthermore to include covariates, and let the effects of the covariates vary with time and space. We consider various types of outcomes including, continuous, categorical and counts. By exploiting kernels for graphs and networks, we show that areal data can be modelled in the same manner as the data that are geo-coded using coordinates. For model estimation, we have implemented both MCMC algorithm and analytical approximations including Laplace approximation and variational inference. In this presentation we demonstrate the proposed methods using empirical data.

Location: SAM.A.323 (S312)

*6 September 2022, 13:00 Stockholm*

Speaker: Associate Prof. Mihai Cucuringu, Department of Statistics, Oxford University, UK.

**Abstract:** We consider the problem of clustering in two important families of networks: signed and directed, both relatively less well explored compared to their unsigned and undirected counterparts. Both problems share an essential common feature: they can be solved by exploiting the spectrum of certain graph Laplacian matrices or derivations thereof. In signed networks, the edge weights between the nodes may take either positive or negative values, encoding a measure of similarity or dissimilarity. We consider a generalized eigenvalue problem involving graph Laplacians, with performance guarantees under a signed stochastic block model setting, along with regularized versions to handle very sparse graphs. The second problem concerns directed graphs. Imagine a (social) network in which you spot two subsets of accounts, X and Y, for which the overwhelming majority of messages (or friend requests, endorsements, etc) flow from X to Y, and very few flow from Y to X; would you get suspicious? To this end, we also discuss a spectral clustering algorithm for directed graphs based on a complex-valued representation of the adjacency matrix, which is able to capture the underlying cluster structures, for which the information encoded in the direction of the edges is crucial. We evaluate the proposed algorithm in terms of a cut flow imbalance-based objective function, which, for a pair of given clusters, it captures the propensity of the edges to flow in a given direction. Experiments on a directed stochastic block model and real-world networks showcase the robustness and accuracy of the method when compared to other state-of-the-art methods. Time permitting, we briefly discuss connections to ranking from pairwise comparisons data, the group synchronization problem, and also overview alternative approaches beyond spectral methods to all the above issues.

Location: SAM.A.323 (S312)

*Time: 17 May 2022, 13:15 Stockholm*

Speaker: Benoît Gozé, doctoral student at the Department of Forest Resource Management, SLU

**Abstract:** In this paper, we investigate methods to estimate plant population size and intensity (also known as density) from presence/absence data. Presence/absence sampling is a useful and relatively simple method for monitoring state and change of plant species communities. Moreover, it has advantages compared to traditional plant cover assessment, the latter being more prone to surveyor judgement error.

We use inhomogeneous Poisson point process models concerning plant locations, and generalised linear models (GLM) with a complementary log-log link function for linking presence/absence data to plant intensity. In these models, auxiliary covariate information coming from remote sensing (i.e. wall-to-wall data) are used. We propose an estimator of plant intensity, as well as a variance of this estimator (and how to estimate this variance). For evaluating these estimators, we use both Monte-Carlo simulations, where we create artificial plant populations, and empirical data from the Swedish National Forest Inventory (NFI). We also develop a test for our models, to check the underlying Poisson point process model assumption and protect inference against model misspecification. The suggested hypothesis test is evaluated through Monte-Carlo. Some models could be produced for a selection of forest plant species and passed the Poisson test. Estimation of plant density and its related variance estimation could be performed for these species.

Location: MIT.A.356 and Zoom

*Time: 10 May 2022, 13:15 Stockholm*

Speaker: Dr Wenjuan Wang, Research Fellow/Senior Data Scientist in the School of Population Health & Environmental Sciences, King’s College London. Dr Wang works on applying machine learning for stroke quality care improvement, as well as for COVID-19 and flu patient management and severity scores.

**Abstract:**

**Part I: Applying machine learning for stroke quality care improvement**

Machine learning was implemented for risk prediction of 30-day mortality after stroke using data from the Sentinel Stroke National Audit Programme (SSNAP) which is the national registry of stroke care in England, Wales and Northern Ireland. The ML model developed more accurately predicted 30-day mortality (AUC 0.896) compared to the previously developed model used in SSNAP (0.854) and was reasonably well calibrated, thus could potentially be used as benchmarking model for quality improvement in stroke care in SSNAP

**Part II: Multivariable analysis of the association of the Alpha variant (B.1.1.7 lineage) of SARS-CoV-2 with disease severity in inner London**

Through a descriptive comparison of admission characteristics between pandemic waves and multivariable analysis of the association of the Alpha variant (B.1.1.7 lineage) of SARS-CoV-2 with disease severity in inner London, we discovered that increased severity of disease associated with the Alpha variant and the number of nosocomial cases was similar in both waves despite the introduction of many infection control interventions before wave 2.

Location: MIT.A.356 and Zoom

*Time: 26 April 2022, 13:15 Stockholm*

Speaker: Henrik Imberg, Doctoral Student, Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg

**Abstract:** Data subsampling has become increasingly used in the statistics and machine learning community to overcome practical, economical and computational bottlenecks in modern large scale inference problems. Examples include leverage sampling for big data linear regression, optimal subdata selection for generalised linear models, and active machine learning in measurement constrained supervised learning problems.

So far, the contributions to the field have been largely focused on computationally efficient algorithmic developments. Consequently, most sampling schemes proposed in the literature are either based on heuristic arguments or use optimality criteria with known deficiencies, e.g. being dependent on the scaling of the data and parametrisation of the model. We develop a general theory of optimal design for data subsampling methods and derive a class of asymptotically linear optimality criteria that i) can easily be tailored to the problem at hand, ii) are invariant to the parametrisation of the model, and iii) enable fast and efficient computation for both Poisson and multinomial sampling designs.

The methodology is illustrated on binary classification problems in active machine learning, and on density estimation in computationally demanding virtual simulations for safety assessment of automated vehicles.

Location: MIT.A.356 and Zoom.

*Time: 22 March 2022, 13:15 Stockholm*

Speaker: Hamed Sabahno, Postdoctoral fellow, Department of Statistics, Umeå University

**Abstract:** Investigating the effects of two real-world-occurring phenomena: 'measurement errors' and 'autocorrelation between observations' on control charts, has caught researchers' attention in recent years. However, their combined effect has rarely been investigated; with only one study for multivariate control charts. In this paper, their combined effects will be investigated for the first time in univariate and multivariate control charts on 'adaptive' and/or 'simultaneous process parameters monitoring' control charts and also for the first time in multivariate control charts by using linearly covariate measurement errors, VARMA (vector mixed autoregressive and moving average) autocorrelation models, and Markov Chain based performance measures. To do so, we add the above-mentioned measurement errors and autocorrelation models to a recently developed adaptive VP (variable parameters) max-type control chart which is capable of monitoring the process parameters simultaneously. Then, we develop a Markov chain model to compute the average and standard deviation of time to chart signal. After developing the control scheme as well as the performance measures in the presence of both measurement errors and autocorrelation, extensive simulation studies will be performed to investigate the combined effects of measurement errors and autocorrelation as well as some methods to alleviate their negative effects. In addition, this paper for the first time uses the skip-sampling strategy in an ARMA/VARMA autocorrelation model for alleviating the autocorrelation effect. At last, an illustrative example involving a real industrial case will be presented.

Location: NAT.D.300 and Zoom

*Time: 1 March 2022, 13:00 Stockholm*

**Microstructures and mass transport in porous materials - combining physics, spatial statistics, machine learning, and data science**

Speaker: Magnus Röding, Adjunct Associate Professor, Chalmers University of Technology and University of Gothenburg, Sweden

**Abstract: **Understanding the microstructure of a porous material and how it relates to its mass transport properties (diffusion, fluid flow) is crucial for designing better materials. One example is coating layers on pharmaceutical pellets for controlled release of compounds, another is liquid transport through fibrous media in hygiene products. We combine e.g. image analysis, spatial statistics, stochastic geometry, numerical simulation techniques, and machine learning to characterize materials and to predict and understand their properties. We will discuss a number of cases involving semantic segmentation of 3D image data, deep learning regression for parameter estimation in different experimental techniques, development of realistic virtual materials models, machine learning-based prediction of properties, and the design of materials with desired properties.

*Time: 22 February 2022, 13:15 Stockholm*

Speaker: Ali Ramazani-Kebrya, a Senior Postdoctoral Associate at EPFL, Switzerland

**Abstract:** To fully realize the benefits of deep learning, we need to design highly scalable, robust, and privacy-preserving learning algorithms along with understanding the fundamental limits of the underlying architecture, e.g., a neural network over which the learning algorithm is applied. The key algorithm underlying deep learning revolution is stochastic gradient descent (SGD), which needs to be distributed to handle enormous and possibly sensitive data distributed among multiple owners, such as hospitals and cellphones, without sharing local data. When implementing SGD on large-scale and distributed systems, communication time required to share stochastic gradients is the main performance bottleneck. In addition to communication-efficiency, robustness is highly desirable in real-world settings. We present efficient gradient compression and robust aggregation schemes to reduce communication costs and enhance security while preserving privacy. Our algorithms currently offer the highest communication-compression while still converging under regular (uncompressed) hyperparameter values. Considering the underlying architecture, one fundamental question is "How much should we overparameterize a neural network?" We present the current best scaling on the number of parameters for fully-trained shallow neural networks under standard initialization schemes.

*Time: 15 February 2022, 13:15 Stockholm*

Speaker: Kreske Ecker, Department of Statistics, Umeå University

**Abstract: **In this work we present methods to study the causal effect of a scalar treatment on a functional outcome based on observational data. We develop a semi-parametric estimator for a Functional Average Treatment Effect (FATE), based on outcome regression. Using recent results from functional data analysis, we show how to obtain exact valid inferences on the FATE under certain conditions: we give simultaneous confidence bands, which cover the parameter of interest with a given probability over the entire domain. Using simulation experiments, we compare the performance of the simultaneous confidence bands to that of pointwise bands that do not take the multiple comparison problem into account, and find that the former achieve the desired coverage rates, whereas the latter do not. In addition, we use the methods presented to estimate the effect of early adult location on subsequent income development for one Swedish birth cohort. Overall, we find a positive effect of living in an urban, as opposed to rural, area at the age of 20 on cumulative lifetime incomes, but there are differences by gender. For women, the effect is stronger and positive over the entire study period, whereas for men there is a negative effect during the first years.

**Location: MIT. A.356 and Zoom**

*Time: 1 February 2022, 13:00 Stockholm*

Speaker: Joakim Walmark, Department of Statistics, Umeå University

**Abstract: **The purpose of equating is to ensure that test scores from different test forms can be used interchangeably. Test forms which include items of different formats, such as dichotomously and polytomously scored items, are typically referred to as mixed-format tests. In this study, the kernel equating method was evaluated under different scenarios for equating of mixed-format tests. In kernel equating, the test score distributions are typically presmoothed to remove irregularities due to sampling before the actual equating is conducted. The use of both log-linear and item response theory (IRT) models for presmoothing were compared through simulations and real data applications. Data was simulated with and without IRT models to avoid exclusively favouring IRT presmoothing and both equivalent and non-equivalent group designs were considered. The simulation results and the real-data applications suggest that using IRT models for presmoothing provides smaller equating standard errors compared to using log-linear models. Additionally, IRT presmoothing resulted in lower bias than log-linear presmoothing when IRT models were used to simulate test data. However, when test data was simulated without the use of IRT models, the bias was lower when log-linear presmoothing was used. In a practical setting, when computation of bias is not possible, using IRT models for presmoothing should be preferred in most situations because of the lower standard errors.

*Time: 25 Janary 2022, 13:15 Stockholm*

Speaker: Niloofar Moosavi, Department of Statistics, Umeå University

**Abstract: **During the last years, a great extent of work has been done on constructing confidence intervals for average causal effect parameters that are uniformly valid over a set of data generating processes even when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These developments assume that all the confounders are observed to ensure point identification. We contribute by showing that valid inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We thus propose uncertainty intervals, which allow for nonzero confounding bias. The later bias is specified and estimated and is function of the amount of unobserved confounding allowed for. We show that valid inference can ignore the finite sample bias and randomness in the estimated value of confounding bias by assuming that the amount of unobserved confounding is small relative to the sample size; the latter is formalized in terms of convergence rates. An interpretation is that more confounders are collected as the sample size grows. Simulation results are presented to illustrate finite sample properties and explore a double selection procedure and a correction of the residual variance estimator, which improve the performance even for larger correlations.

2021

**Prehospital resource optimization, February 2**

Speaker: Patrik Rydén, Department of Mathematics and Mathematical Statistics, Umeå University

The prehospital care in Sweden has about 660 ambulances, respond to about 1.2 million emergency calls per year, and costs more than 4 billion SEK per year. An aging population, urbanization and medical progress demand a flexible prehospital care. The goal of this project is to develop processes and tools that make it possible to organize ambulance units and operations in an optimal way. Based on big and complex alarm-data, advanced statistical modelling and large-scale data driven simulations we have develop tools to compare allocations (how the ambulances are placed and scheduled) under user defined future scenarios. The solution makes it easy to highlight the implications for specific regions and patient groups. The next step is to find the allocation that optimize some user defined loss function. Here an allocation can be thought of as a design point in a high-dimensional space for which the loss can be estimated using time demanding simulations and where the design points can be selected iteratively. I will give an overview of the project and highlight some interesting problems and results.

**162 years of temperatures in Umeå, 1859-2020, February 16 **

Speaker: Per Arnqvist, Department of Mathematics and Mathematical Statistics, Umeå University

**Maximum likelihood estimation in stochastic channel models**

Speaker: Christian Hirsch, University of Groningen, February 23

We propose Monte Carlo maximum likelihood estimation as a novel approach in the context of calibration and selection of stochastic channel models. First, considering a Turin channel model with inhomogeneous arrival rate as a prototypical example, we explain how the general statistical methodology is adapted and refined for the specific requirements and challenges of stochastic multipath channel models. Then, we illustrate the advantages and pitfalls of the method on the basis of simulated data. Finally, we apply our calibration method to wideband signal data from indoor channels.

Based on joint work with Ayush Bharti, Troels Pedersen, Rasmus Waagepetersen'

**Global envelopes with applications to functional data analysis and general linear model, March 2**

Speaker: Mari Myllymäki, Natural Resources Institute Finland (Luke), Helsinki, Finland.

Abstract: Global envelopes are nowadays quite often used in testing null models for spatial processes by means of different summary functions, because they provide a formal test and provide suggestions for alternative models through graphical interpretation of the test results. Global envelopes are however a rather general tool that can be applied in various applications. Namely, they can be employed for central regions of functional or multivariate data, for graphical Monte Carlo and permutation tests where the test statistic is multivariate or functional, and for global confidence and prediction bands. In this talk, I describe the global envelopes, illustrate the methodology on different applications including the functional general linear model, and show examples of the usage of the R package GET (Myllymäki and Mrkvička, 2020) that implements global envelopes. Further, I discuss the multiple testing correction in the global envelope tests for functional test statistics, which are discretized to m highly correlated hypotheses. While the global envelopes were first developed to control the family-wise error rate, also control of false discovery rate can be introduced.

Myllymäki and Mrkvička (2020). GET: Global envelopes in R. arXiv:1911.06583 [stat.ME] https://arxiv.org/abs/1911.06583

**Summary statistics for point processes on linear networks, March 30**

Speaker: Mohammad Mehdi Moradi, Department of statistics, computer sciences, and mathematics, the public university of Navarra, Pamplona, Spain.

Abstract: The last decade witnessed an extraordinary increase in scientific interest in the analysis of network-related data. This pervasive interest is partly caused by a strongly expanded availability of such datasets. In the spatial statistics field, there are numerous real examples, such as the locations of traffic accidents or street crimes, with the need of restricting the support of the underlying process over the corresponding network structure to set and define a more realistic scenario. This being said, the analysis of the point process on a linear network has been extremely challenging due to the geometrical complexities of the network. In this talk, we go through summary statistics of different orders, and their estimators, to study the correlation between events that occurred over a linear network. We highlight the importance of the change-of-support, mathematical challenges, and the use of different distance metrics would be also discussed. Finally, we demonstrate applications to traffic accidents and criminology.

**Stochastic analysis and modelling of eye movements, April 20**

Speaker: Aila Särkkä, Professor at the Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, Sweden.

Abstract: Eye movements are outcomes of cognitive processes in the human brain, and can be recorded with a high spatial and temporal resolution by computerized eye trackers. Here, the question of interest is how people look at art. The data come from a cognitive art research experiment, where the eye movements of twenty test subjects were recorded while they were looking at six paintings, each painting for three minutes. We will concentrate on studying the eye movements on one of the six paintings, namely Koli landscape by Eero Järnefelt.

Eye movements can be represented as an alternating sequence of fixations (periods in which the gaze is staying relatively still around a location of the target space) and saccades (rapid movements between the fixations). We regard the process of fixations as a spatio-temporal point process and introduce methods to analyse the point pattern data and models for the spatio-temporal eye movement process including fixation locations, fixation durations, and saccade durations and lengths. I will mainly discuss joint work with Anna-Kaisa Ylitalo and Peter Guttorp [1] but will also briefly mention the work by Antti Penttinen and Anna-Kaisa Ylitalo [2].

References:

[1] Penttinen, A., and Ylitalo, A.-K. Deducing self-interaction in eye movement data using sequential spatial point processes. Spatial Statistics 17, (2016), 1-21.

[2] Ylitalo, A.-K., Särkkä, A. and Guttorp, P. Stochastic analysis and modeling of eye movements in viewing paintings. Annals of Applied Statistics 10(2), (2016), 549-574.

**Train performance analysis using heterogeneous statistical models, June 8**

Speaker: Jianfeng Wang, First research engineer, Department of Mathematics and Mathematical Statistics, Umeå University

**On the rate of convergence of deep neural network regression estimates, September 20**

Speaker: Dr. Sophie Langer, TU Darmstadt, Germany

Abstract: Recent results in nonparametric regression show that deep learning, i.e., neural network estimates with many hidden layers, are able to circumvent the so–called curse of dimensionality in case that suitable restrictions on the structure of the regression function hold. Under a general composition assumption on the regression function, one key feature of the neural networks used in these results is that their network architecture has a further constraint, namely the network sparsity. In this talk we show that we can get similar results also for least squares estimates based on simple fully connected neural networks with ReLU activation functions. Here either the number of neurons per hidden layer is fixed and the number of hidden layers tends to infinity suitably fast for sample size tending to infinity, or the number of hidden layers is bounded by some logarithmic factor in the sample size and the number of neurons per hidden layer tends to infinity suitably fast for sample size tending to infinity. In a second result we show that deep neural networks (DNNs) achieve a dimensionality reduction in case that the regression function has locally low dimensionality. Consequently, the rate of convergence of the estimate does not depend on its input dimension d, but on its local dimension d* and the DNNs are able to circumvent the curse of dimensionality in case that d* is much smaller than d.

**Resample-smoothing and statistical learning for point processes, October 28**

Speaker: Mehdi Moradi, Public University of Navarre, Spain

Abstract: The analysis of point patterns may almost always begin with estimating the intensity function due to its control over distributional behaviours of the underlying point process that is assumed to have generated the observed pattern. Going through the literature, one can easily see that many techniques, based on different points of view, have been proposed for intensity estimation. In this talk, by employing independent random thinning, we show how i) a resample-smoothing approach can significantly improve the performance of Voronoi intensity estimators, and ii) a statistical-learning-based approach enhances kernel-based intensity estimators. We discuss technical details, and through simulation studies show how our proposals improve the state-of-art. Applications to some real data will also be presented.

References:

Cronie, O., Moradi, M., and Biscio, C. A. (2021). Statistical learning and cross-validation for point processes. arXiv preprint arXiv:2103.01356.

Moradi, M., Cronie, O., Rubak, E., Lachieze-Rey, R., Mateu, J., and Baddeley, A. (2019). Resample-smoothing of Voronoi intensity estimators. Statistics and computing, 29(5), 995-1010.

2018

**19 September, 13:15, Hörsal E Humanisthuset**

Angel G. Angelov, Department of statistics Umeå University

Methods for interval-censored data and testing for stochastic dominance

**9 October, 13:00 - 14:00, UB334**

Giovanni Forchini, School of Business Economics and statistics Umeå University

Ill-Conditioned Problems and Fisher Information

**16 October, 13:00 -14:00, UB333**

Raoul Theler, School of Business, Economics and statistics Umeå University

On the Evaluation of Endogenous Treatment Effects Correlated with Natural Instruments

**13 November, 13:00 - 14:00, UB334**

Xuan-Son Vu, Department of computer science

Privacy in the world of AI and Big data

**20 November, 13:00 - 14:00, UB336**

Mohammad Ghorbani, Department of Mathematics and Mathematical Statistics

Statistical analysis of functional marked point processes

**27 November, 13:00 - 14:00, UB336**

Maria Josefsson, Centre for demographic and aging research Umeå University

Bayesian semiparametric G-computation for causal inference in a cohort study with non-ignorable dropout and death

**4 December, 11:00 - 12:00, UB337**

Juha Karvanen, Jyväskylä University Finland

Combining experiments and observations in causal inference

**19 December, 13:15-14:00, UB337**

Tetiana Corbach, Department of statistics Umeå University

Bayesian mixture modeling of fMRI connectivity in cross-sectional and longitudinal studies.