SPMS 2022

23 Jun 2022, 11:00 → 27 Jun 2022, 12:00 Europe/Prague

Jiří Franc (The Czech Technical University in Prague), Václav Kůs (KM FJFI CVUT)

The Stochastic and Physical Monitoring Systems (SPMS) has been an annual international conference since 2010 with the aim to bring together students and researchers with areas of interest related to the following topics:

• Traffic and pedestrian modeling, microscopic structure of vehicular streams.
• Elasticity and classification in material defectoscopy;
• Small area estimation and Generalized mixed linear model;
• Data analysis in particle and experimental physics.
• Stochastic models, Bayesian analysis, competitive games.

The meeting is organized by the Group of Applied Mathematics and Stochastics (GAMS), Department of Mathematics, Czech Technical University in Prague.

The SPMS 2022 conference will be held at Hotel SportLife, Rumburk, Czech Republic from 23th to 27th of June, 2022.

SPMS2022_instructions.pdf

SPMS2022_paper_template.zip

SPMS2022_poster_v3_small.pdf

Thursday, 23 June

11:00 → 14:00 Registration with Lunch

14:00 → 14:15 Welcome speach

14:15 → 15:40 Stochastic Monitoring Systems

Convener: Jiří Franc (Czech Technical University (CZ))

14:15 Generalized linear mixed models for small area estimation

This contribution deals with a possible use of statistical models for estimating characteristics of some geographical regions, called “small areas”. More concretely, estimation of a given function of an income variable, like e.g. average incomes or poverty proportions, is considered. As the variable income has an asymmetric distribution, it is not properly modelled via normal distributions. When dealing with this type of variables, a first option is to apply transformations that approach normality. A second option is to use non-symmetric distributions like the gamma distribution. This contribution proposes a unit-level gamma mixed model for modelling positive variables and derives three types of predictors of small area additive parameters, called empirical best, marginal and plug-in. The mean squared errors of the predictors are estimated by a parametric bootstrap. Some results of simulation experiments studying the behavior of the estimator of the mean squared errors are presented. By using data of the Spanish living condition survey of 2013, an application to the estimation of average incomes and poverty proportions in counties of the region of Valencia is given.

Speaker: Tomáš Hobza (Department of Mathematics, FNSPE, Czech Technical University in Prague )

SPMS2022_Hobza.pdf

14:40 Ising Model of Ferromagnetism

This paper is divided into three parts. In the first chapter, the basic aspects of the Ising model are explained and the solution of both one-dimensional and two-dimensional versions of this model is presented. In the case of solving the model in 2D, two different solutions are compared. In the second chapter, Markov Chain Monte Carlo methods are briefly presented. The third part of the paper follows the previous two parts with practical simulations, as it presents the solution of the Ising model in 1D, 2D, and 3D, always on a square grid. The simulations are then tested on other grids, namely in the case of the two-dimensional version on hexagonal and triangular grids. This chapter also includes an investigation of the critical temperature of each configuration.

Speaker: Jan Trödler (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_Trodler_prezentace.pdf

15:00 Estimating Sparse Parameterization of Neural Networks

The paper deals with methods for estimating sparse parameterization of neural networks, which can be used to prune overparameterized neural networks and reduce their complexity in an attempt to reveal only relevant parameters, thus increasing the overall interpretability of the model. In this paper, the classical and the variational methods, which allow these parameterizations to be estimated, are described. This is achieved by reviewing special prior distributions, here referred to as shrinkage priors, which allow us to incorporate our preferences about sparse parameterizations into the model. Variational methods then help us to approximate the posterior distribution for model parameters. Using this posterior distribution, it is possible to better quantify the uncertainty of the parameters. Finally, the methods are applied to various models, including linear and logistic regression, neural networks, and are also utilized in the concept of multi-instance learning. The experiments are carried out on both synthetic and real data.

Speaker: Lukáš Kulička (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_Kulička_presentation.pdf

15:20 Hybrid Discriminative-Generative Training for Set data

This contribution deals with hybrid discriminative and generative models and their possible use in multi--instance learning, where one sample consists of a set of vectors. So far, these models have only been trained discriminatively. However, it turns out that the discriminative approach alone can have downsides and, by adding a generative component, these downsides can be minimized. There are several ways to include a generative component in model training. We focus on two, one using contrastive learning and the other based on a variational autoencoder. The mainstay of working with set data is then the HMill framework with the Mill.jl library, implemented in the Julia programming language, which allows us to train models on these data simply and efficiently. We will try to extend it with a generative component.

Speaker: Jakub Bureš (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Prezentace_SPMS_Bures (1).pdf

15:40 → 16:00 Coffee break

16:00 → 16:30 Erasmus+

16:00 Zkušenosti z Erasmus+ pobytu v Grenoblu - studium, země, lidé... (hory)

V prezentaci ukážeme campus univerzity v Grenoblu, promluvíme o studovaných předmětech, jejich kvalitě a obtížnosti složení zkoušek, o typu semestrů a odlišnosti zkouškového období. Dále budeme komentovat vztahy místních studentů a jejich studentské společenské aktivity. Na závěr ukážeme fotky ze studentských výletů. Během přednášky se předpokládá interaktivní neformální atmosféra.

Speaker: Jan Zavadil

SPMS22_Erasmus in Grenoble.pdf

16:30 → 19:00 Outdoor Discussions & Consultations

19:00 → 20:00 Dinner

Friday, 24 June

09:00 → 10:20 Dynamic Decision Making

Convener: Jaromír Kukal (FNSPE CTU in Prague)

09:00 User's Feedback in Preference Elicitation

The research studies optimal decision-making with the focus on preferences quantified for fully probabilistic design (FPD). FPD models the closed DM loop and the agent’s preferences by joint probability densities (pds). There is a preference-elicitation (PE) principle, which maps the agent’s model of the state transitions and its incompletely expressed wishes on an ideal pd quantifying them. This research also studies preferences targeting actions and contradicting preferences.
The gained algorithmic quantification provides ambitious but potentially reachable DM aims.
It suppresses demands on the agent selecting the preference-expressing inputs (a set of preferred states and preferred actions). The remaining PE options are: a parameter balancing exploration with exploitation; a fine specification of the ideal (desired) sets of states and actions; relative importance of these ideal sets.
In addition to the above, we add a meta-DM task to learn the user’s (agent’s) preferences and be able to find the free parameters optimally. The algorithmic “meta-agent” observes user’s satisfaction, expressed by school marks from 1 to 5 as in school and tunes the free PE inputs to improve these marks as much as possible. The solution requires a suitable formalisation of such a meta-task.
In my presentation, I will describe the principles of the meta-task and show experiments with feedback from different users and summarize improvements and shortcomings of the theory.

Speaker: Tereza Siváková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Sivakova_SPMS.pdf

09:20 About Use of Everett’s Interpretation of Quantum Mechanics for Decision Making

Modern decision making (DM) theory stands on classical probability. But there seems to be a variety of situations when the decision theory fails to explain some psychological and cognitive effects observed in human decision making.
Other aspects not covered by the classical approach are that the results of merging information depend on the order of merging, or that the observation influences the next state.
Main question posed is whether quantum probability is suitable for DM and can solve these problems.
The contribution tries to formulate a decision making task by using Everett's many-worlds interpretation of quantum mechanics.
The targeted long-term perspective is to use Everett's interpretation to develop a quantum version of fully probabilistic design of decision strategies. The presentation will cover the very preliminary results.

Speaker: Aleksej Gaj (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_22_AG_final.pdf

09:40 Dynamic decision making with stopping

Decision making (DM) is one of the key challenges since it appears in fields of study across all disciplines. The Fully Probabilistic Design of decision policies (FPD) represents an extension of well established decision making method using Markov Decision Processes (MDP). Both of these theories studies and try to model the evolution of states in the closed-loop through studying of transition probabilities. FPD and MDP aim to select proper policy consisting of sequences of action-generating decision rules. Sequence of states and actions generated by the closed-loop up to the finite horizon is called behaviour. The joint probability distribution (pd) of behaviours is the product of state-transition probabilities and decision rules. Agent who uses the MDP approach constructs a reward function over the state and action space. Goal of the agent is to maximise the expected reward. The expectation depends on the discussed joint pd. The main difference between FPD and MDP is that FPD quantifies agent's aims and restrictions via use of ideal state-transition probabilities and ideal decision rules, instead of rewards. These ideal probabilities and decision rules form the ideal joint pd of behaviours. The joint ideal pd is describing closed-loop and reflects satisfaction with each behaviour. The ideal pd is high for behaviours that the DM agent desires, small for unwanted behaviours and zero for the prohibited ones. The optimal policy in FPD minimises the Kullback-Leibler divergence of the behaviour-modelling pd to its ideal counterpart. FPD generalises MDP but due to its much shorter history, the FPD theory lacks elaborating of many tasks already solved within MDP. The paper addresses such a problem, namely, the problem of finding the optimal stopping rule while exploiting the FPD approach. This problem is related to a broader range of DM tasks that use mix of continuous and discrete valued actions.

Speaker: Daniel Karlík (Department of Adaptive Systems, Institute of Information Theory and Automation, Czech Academy of Sciences)

SPMS_DanielKarlik.pdf

10:00 Learning State Correspondence of Reinforcement Learning Tasks for Knowledge Transfer

Deep reinforcement learning has shown an ability to achieve super-human performance in solving complex reinforcement learning tasks only from raw-pixels. However, it fails to reuse knowledge from previously learnt tasks to solve new, unseen ones. To generalize and reuse knowledge is one of the fundamental requirements for creating a truly intelligent agent. The work summarizes the problem of transfer learning in reinforcement learning tasks and offers a method for one-to-one task transfer learning.

Speaker: Marko Ruman (Department of Mathematics, FNSPE, Czech Technical University in Prague)

presentation_1.pdf

10:20 → 10:40 Coffee break

10:40 → 12:10 Traffic and Agent Monitoring Systems Session

Convener: Tomáš Hobza (FJFI CVUT)

10:40 The properties of scaled GIG distribution

The Generalized Inverse Gaussian distribution (GIG) has become popular in recent decades, mainly in the area of vehicular headway modelling. As a part of the investigation of the GIG’s scaling function approximation, computations in the research have revealed key relationships among distribution’s parameters and properties of the scaling function that have often been assumed, but never mathematically proven. The new findings support the GIG distribution research in various other aspects as well as providing a better understanding of the scaling problem.

Speaker: Anežka Lhotáková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_2022_Lhotakova.pdf

11:00 Statistical models for estimation of unsignalized intersection capacity

Critical clearances are the main subject of the Gap Acceptance theory, which is the basis for analytical derivation solving theoretically a problem of vehicular capacity estimations for unsignalized intersections. The applied statistical method is based on the generally accepted practice formulated by Werner Siegloch, who introduces the concept of the Siegloch function. With the premise of GIG-distributed clearances and critical clearances, in the considered model of an unsignalized T-intersection, the approximation of the Siegloch function is derived and the suitable alternative of this theoretical approximation is proposed. In addition to that, it is shown that the traditional regression technique fails and the verified methodology based on a thoughtful application of contemporary regression methods is discussed.

Speaker: Eliška Pečenková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Eliška_Pečenková_SPMS_2022.pdf

11:20 Crash! Boom! Bang!

Our research is focused on stochastic modeling of vehicular dynamics in the vicinity of an unsignalized intersection of the T-type. The paper converts the standardly-applied engineering method of the critical gap (which represents the minimum time clearance between two succeeding vehicles in the priority stream that a minor-street driver is willing to accept for entering the major stream) into a purely mathematical form operating strictly in the language of random variables. The main contribution therefore consists in the mathematical formalization of the gap-acceptance problem, which allows to reveal an implicit gap-acceptance decision rule. The main goal of this article is to introduce the mathematical model, show methods for measuring, analyzing, and evaluating empirical traffic data. Furthermore, we discuss interesting mathematical aspects of the topic.

Speaker: Michaela Krbálková (FS University of Hradec Králové, FTE University of Pardubice)

Crash! Boom! Bang!_final_version.pdf

Crash! Boom! Bang! final_version.pptx

11:40 Density Estimates in Cellular Automata Models of Pedestrian Dynamics

Presented contribution deals with general concept of pedestrian density estimate appropriate even for cellular models of pedestrian dynamics. Using kernel approach, authors are able to cover multiple density estimate methods (e.g. point approximation, Voronoi approach) and to control required features by "blur" parameter. With respect to specific setting, final density can be smooth enough even for discreet lattice and still keep other requirements.

Speaker: Marek Bukáček (Czech Technical University in Prague)

prez_spms_buk_v2.pdf

12:00 The Importance of Being Local

To understand pedestrian behavior properly, it is necessary to read the information hidden in measured (experimental) data in an appropriate way. It means that the estimate of any quantities describing a phase of the system has to be evaluated intentionally and incorporate specificities of the given data. In this paper, we deal with measuring a fundamental quantity in socio-physical systems, the density, focusing on the differences between local (dynamic detector) and global estimates (static detector). Moreover, we discuss several ways how to take the local aspect into account – to do that, different shapes and sizes of pedestrian surroundings are analyzed.

Speakers: Jana Vacková (Department of Mathematics, FNSPE, Czech Technical University in Prague), Marek Bukáček (Department of Mahtematics, FNSPE, Czech Technical University in Prague)

12:30 → 13:30 Lunch

14:00 → 15:05 Defectoscopy and Physical Monitoring Systems

Convener: Václav Kůs (KM FJFI CVUT)

14:00 Application of neural networks for acoustic emission method

Artificial neural networks have been used in acoustic emission signal processing for a long time. In recent years, however, the application capabilities of machine learning have been significantly expanded due to the development of modern architectures of artificial intelligence. Since the early tests of feed-forward neural networks to account for the anisotropy of elastic wave propagation velocity in materials and the success in locating emission sources, modern architectures have now been applied directly to continuous emission signals to monitor material damage processes.

Speaker: Milan Chlada (Institute of Thermomechanics, Czech Academy of Sciences)

SPMS-2022-presentation-Chlada.pdf

14:25 Signal Event List Generation Using Neural Networks

The goal of this paper is to summarize deep learning methods and to apply the gained knowledge on signal decomposition and signal event detection tasks. In the first part several architectures are applied to a continuous signal in order to estimate its original components corresponding to the individual sources. Several metrics are used in order to evaluate the final models. In the second part the strategy for signal events detection in the input signal is discussed. The potential of these methods is demonstrated both on a musical dataset and on burst acoustic emission originating from material fatigue tests. The trained neural networks can be used to automate the analysis of ultrasonic signals, e.g. for real-time detection of emission events.

Speaker: Martin Kovanda (Department of Mathematics, FNSPE, Czech Technical University in Prague)

Kovanda_Presentation.pdf

14:45 Classification of AE Signals Based on Statistics and Machine Learning

Reliable classification of acoustic emission signals is crucial for practical use of this nondestructive testing technique. During the classification, signals can either be represented by a convenient, low-dimensional set of attributes or passed in their entirety to the classification algorithm. This contribution adresses the problem of selecting efficient attributes for classification and consequently describes and compares several classification methods. Results of chosen classification methods on laboratory measured data are presented and the methods are compared.

Speaker: Jan Zavadil (Department of Mathematics, FNSPE, Czech Technical University in Prague)

SPMS_22.pdf

15:05 → 15:30 Coffee break

15:30 → 17:00 Defectoscopy and Physical Monitoring Systems

Convener: Václav Kůs (KM FJFI CVUT)

15:30 Ultrasonic techniques used to nonlinearity characterization of humanSkin /in-vivo

The talk will serve as an Introduction to both the following lectures of the french students from the Institute of Thermomechanics AV ČR. We deal with the techniques and methods used in in-vivo skin elasticity characterizations. Precise measurements on skin flexibility is needed and thus we focus on mechanic properties of human skin and very delicated measurement techniques.

Speaker: Zdeněk Převorovský (Institute of Thermomechanics, Czech Academy of Sciences)

16:00 Novel design of a device for measurement of human skin viscoelastic properties

Human skin has a complex mechanical behavior which can be described as anisotropic and non-linearly viscoelastic. These properties are not well determined but they are of great interest e.g. in cosmetic industry and aesthetic medicine.
This paper deals with a novel design of a device which measures the mechanical characteristics of the skin in-vivo, in particular the detailed mechanical design of the prototype device using 3D-printed components. The design of necessary mechanical components deals with a loading base in which are integrated ultrasonic transducers in order to transmit and receive ultrasonic signals propagating in the loaded skin. The loading base is built up with displacement sensor for the purpose of measurement of mechanical loading of the skin. The design of mechanical parts also includes a specific component integrating strain-gauges sensors in order to obtain the stress-strain of the skin tissue.
Subsequent to the assembly of the whole device, verification of the mechanical components ensures the coherence of the entire design. The future work will be focused on electrical conception of the device for the motor control, strain-gauges and displacement sensor for stress-strain measurements, and finally the calibration and tests of the device in its complexity.

Speakers: Flavie Delouye (Institute of Thermomechanics, Czech Academy of Sciences), Perrine Bégon (Institute of Thermomechanics, Czech Academy of Sciences)

Novel design of a device for measurement of human viscoelastic properties.pdf

Novel design of a device for measurement of human viscoelastic properties.pptx

16:25 Multiscale Statistical Identification of Skin Nonlinear Characteristics in the Time Domain

Much research has been conducted on the characteristics of skin and collagen as one of the skin's main components at the micro-scale. However, there are limited studies on the mechanical behavior of biomaterials such as skin at the macro-scale. This is due to the complexity of their structure and various characteristics that are dependent on a huge range of parameters. Gaining knowledge on this matter provides the investigation of biomaterial characteristics and aging processes.
In this context, an experimental setup based on stress induced on skin by airflow and captured by fast acquisition camera (300 Hz) is utilized. This enables the extraction of new multiscale statistical parameters such as relaxation characteristics in the time domain using the Preisach-Mayergoyz (PM) space. During current study, the characteristics of the system and biomaterial are extracted by applying data and image processing procedures to the experimental outcomes in order to evaluate the nonlinear behavior of the skin. It allows the development of a model that describes the subject's parameters.

Speaker: Parnian HEMMATI (Sharif University of Technology, Teheran, Iran + INSA Centre Val de Loire; U1253 iBrain Inserm-Universit\'e de Tours, Blois, France)

SPMS2022_ParnianH_f.pdf

SPMS2022_ParnianH_f.pptx

17:00 → 19:00 Outdoor Discussions & Consultations

19:00 → 20:00 Dinner

Saturday, 25 June

09:00 → 18:00 Whole day trip to discover Bohemian-Saxon Switzerland NP

Depends on Weather

19:30 → 22:30 Conference Dinner Round the Fire

Sunday, 26 June

09:15 → 10:25 Applied Statistical Methods

Convener: Tomáš Hobza (FJFI CVUT)

09:15 Fast Evaluation of Modified Renyi Entropy for Fractal Analysis

A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional grid based methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented here as the modified Renyi entropy $H_\alpha^*$. A novel approach that employs the log-linear dependence of a modified Renyi entropy is used together with very fast implementation of $\epsilon$ search in k-d tree.

Speaker: Jaromír Kukal (Department of Software Engineering, FNSPE, Czech Technical University in Prague)

ROTATIONALSPECTRUMD2.pdf

SPMS2022RENYIDIMENSION.pdf

TRINVARRENYIDIM.pdf

09:40 A New Distribution Derived with Maximum Renyi Entropy Principle for Returns of Financial Assets

We derive a new distribution using maximum Renyi entropy principle under the absolute moment constraints. The newly derived distribution has four parameters: two shape parameters and location and scale parameters. The density of this distribution is smooth and twice differentiable which allows its parameters to be estimated by maximum likelihood estimation method. It is clear from its density that this distribution can capture the heavy tail property of returns of financial assets. We verify the ability to model returns of financial assets on various types of assets and compare it with the one of other heavy tail distributions often used for this purpose. This distribution seems to be a dominant alternative to its competitors.

Speaker: Quang Van Tran (Department of Software Engineering , FNSPE, Czech Technical University in Prague)

SPMS2022Q.pdf

Tran_Kukal_Paper_in_FRL.pdf

10:05 Oscillatory Properties of Fractal Diffusion

The contribution presents the statistical properties of the diffusion process over fractal sets represented as sparse grids. The summary of differences between regular and sparse grid diffusion is presented together with an overview of dimension estimation methods. The main focus is on less than one-dimensional sets which allow for the analytical study of return probability. Oscillatory properties of sparse grid diffusion are demonstrated using simulation data and an improved dimension estimation method is shown.

Speaker: František Gašpar (Department of Software Engineering, FNSPE, Czech Technical University in Prague)

SPMS2022.pdf

10:25 → 10:45 Coffee break

10:45 → 11:50 Data Analysis and Deep Learning

Convener: Jiří Franc (Czech Technical University (CZ))

10:45 Deep Learning in High Energy Physics

Deep learning is a type of a broader family of machine learning models that uses artificial neural networks for extracting abstract features from the raw inputs. High energy physics tasks often profit from the application of deep learning techniques thanks to the amount of training data produced by Monte Carlo simulations and particle detectors. Because of the large amount of processed data, model latency is a crucial metric for a successful deployment. In this talk, we present a use case of a deep learning model for fast data segmentation and we discuss techniques leading to improving the latency of the model.

Speaker: Miroslav Kubů (CERN)

11:10 Ensemble model for detector simulations

Detector simulations are indispensable for new HEP discoveries. However, the standard step-by-step Monte Carlo simulation tools are very time-consuming and soon will become intractable. In this talk, we present an ensemble model of generative adversarial networks applied to calorimeter images, as an example of a deep learning-based approach to simulations.

Speaker: Kristina Jarůšková (Department of Software Engineering, FNSPE, Czech Technical University in Prague)

kj_spms2022.pdf

11:30 Deep Learning in Zero-shot Blind Image Deconvolution

The aim of blind image deconvolution is to recover a sharp image from a blurred one. Assuming that there is no other data than one blurred image, the problem is highly ill-posed. Many methods were proposed, yet there is none that would be 100% reliable. Approaches based on bayesian models that attempt to describe image statistics using priors had played major role in zero-shot blind image deblurring until a deep image prior (DIP) and subsequently a DIP framework for blind image deconvolution were proposed. Possible reasons why they outperform traditional blind image deblurring methods will be discussed in this presentation.

Speaker: Antonie Brožová (Department of Mathematics, FNSPE, Czech Technical University in Prague)

init_blind_deconv.pdf

12:30 → 13:30 Lunch

14:00 → 14:40 Defectoscopy and Physical Monitoring Systems

14:00 Comparison of Classification Methods in Acoustic Emission Signals Classification

Acoustic Emission (AE) testing is one of very important methods of non-destructive material testing. Measured signal of AE can have its origin not only in a defect of material, but also it can be caused by noise in material. From this reason it is necessary to classify measured AE signals. For classification we use several classification methods as, for example, fuzzy method, Support Vector Machines, Model Based Clustering, Decision Trees, etc. It is not possible to compare whole signals, therefore we extract different signal parameters from each AE signal. In classification methods and also in extraction of parameters we use different types of phi-divergence. We compare classification methods together with AE parameters in order to obtain an optimal process of AE signals classification.

Speakers: Václav Kůs (Department of Mathematics, FNSPE, Czech Technical University in Prague), Zuzana Dvořáková (Department of Mathematics, FNSPE, Czech Technical University in Prague)

14:20 PM space machine learning based evaluation of material properties

The mixture of probability densities are identified for hysteretic material reprezented in its Preisach-Mayergoyz (PM) space, based on measured hysteresis curve. First, the theoretical description of hysteresis and its PM model are introduced. The heuristic optimization algorithm called aDE-Jaya is employed in order to optimize the parameters of every density components. These components are identified through tree-based machine learning methods, as well as by means of more sophisticated deep and convolutional neural network methods. All the methods are firstly implemented to classify the best-fitting probability distribution from the hysteresis distribution and secondly implemented to regress the representation of the individual components in the mixture of distributions. For an evaluation of the elastic properties of materials, the kernel estimators with special 2D fitted supports are applied to PM space. After comprehensive testing, all the methods are applied to the real data measured on steel earthquake dampers.

Speakers: Erik Dolejš (Department of Mathematics, FNSPE, Czech Technical University in Prague), Václav Kůs (Department of Mathematics, FNSPE, Czech Technical University in Prague)

14:40 → 15:40 Stochastic Monitoring Systems

Convener: Václav Kůs (KM FJFI CVUT)

14:40 Numerical comparison of selected variants of MDEs

The contribution focuses on minimum distance density estimators $\widehat{f}_n$ of the true density $f_0$ on the real line. Our numerical simulation illustrates the quality of consistency property covered by theoretical results (known from prewious work) for sample sizes from $n=10$ to $n=500$. The proportionality constants of the consistency order are estimated from simulated data since they are not given by the proofs of theorems. Dependence of consistency in L$_1$ norm on $\varepsilon$--contamination neighbourhood of the true model is studied and further the robustness of theses newly defined estimator for contaminated normal family is investigated. Numerical simulations are used to compare statistical properties of Kolmogorov, Cramér--von Mises, generalized Cramér--von Mises, and Kolmogorov--Cramér and to determine the optimal or preferable choice of parameters of newly defined estimators. Final comparison brings results for robustness and empirical relative efficiency of Kolmogorov, Cramér--von Mises, generalized Cramér--von Mises, Kolmogorov--Cramér (with preferable choice of parameters) estimators together with Rényi, power divergence, and maximum likelihood estimators.

Speaker: Jitka Hrabáková (FIT CVUT)

14:55 Prediction of the imbalance in the power system

This work deals with the application of stochastic control methods for trading on power markets. It acquaints readers with the basics of the functioning of the electronic exchange and with the specifics of the energy market. This is followed by the theory of stochastic differential equations and stochastic optimal control. The objective is to understand the current results in the field of optimal trading on the energy exchange, which includes the implementation of a suitable numerical scheme to solve the Hamilton–Jacobi–Bellman equation, and come up with a modification of the solution that would include current real business aspects and constraints in the energy market.

Speaker: Filip Mairinger (Department of Mathematics, FNSPE, Czech Technical University in Prague)

15:10 Machine Learning Methods for Power Markets

Along with the growing share of renewable energy sources together with pan European integration of day-ahead and intraday electricity markets, volatility in all kind of energy markets has been increasing in recent years. Increased liquidity in intraday markets helps to minimize deviations and stabilize the transmission system, and in long-term markets it helps to hedge contracts. With this increasing number of trades, market participants, and huge amount of data, the possibility to use machine learning models and neural networks for trading also comes into play. This text focuses on the research of these models and their implementation in energy markets. The aim is to process available data from energy markets and weather data from Europe and to explore possible correlations. The next goal is to prepare and train a robust model and verify it on recent data. The implementation of a solution for time series on algorithmic trading is an upcoming task of this work.

Speaker: Vojtěch Obhlídal

15:25 Emergence of Novelty in Evolutionary Algorithms

Evolutionary algorithms are based on basic ideas of natural evolution
as selection, mutation and reproduction. These algorithms often converge into local
optima and fail to  nd a global goal or solve the underlying task at hand. One of
the solutions presented in the literature to this problem is Novelty Search. Instead
of rewarding agents based on a carefully crafted  fitness function, Novelty Search
rewards agents based on how novel their behaviour is. This research paper presents
a new algorithm, Sugar Search, which also rewards agents for original and novel
behaviour. Further, this paper includes the  first step in generalizing Sugar Search called Pixel Novelty. Experiment results show that both new approaches score as good as or better than Novelty Search in many cases.

Speaker: Dominika Zogatová

15:40 → 16:00 Coffee break

Monday, 27 June

09:00 → 10:00 Closing Remarks & Evaluation of the Conference

10:00 → 12:00 Departure of all Participants