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VERSION:2.0
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BEGIN:VEVENT
SUMMARY:PAC-Bayes training for neural networks: sparsity and uncertainty q
uantification
DTSTART;VALUE=DATE-TIME:20220803T150000Z
DTEND;VALUE=DATE-TIME:20220803T152000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1238@conference2.aau.at
DESCRIPTION:Increasing computational power and storage capacity have made
high-dimensional datasets accessible to many areas of research such as med
icine\, natural and social sciences. While classical statistical methods a
re not compatible with high-dimensional data\, especially due to the curse
of dimensionality\, machine learning methods have been successfully appli
ed to regression problems in practice. On the theoretical level\, a popula
r way to circumvent the curse of dimensionality is the concept of sparsity
. We study the Gibbs posterior distribution from PAC-Bayes theory for spar
se deep neural nets in a nonparametric regression setting. To access the p
osterior distribution\, an efficient MCMC algorithm based on backpropagati
on is constructed. The training yields a Bayesian neural network with a jo
int distribution on the network parameters. Using a mixture over uniform p
riors on sparse sets of network weights\, we prove an oracle inequality wh
ich shows that the method adapts to the unknown regularity and hierarchica
l structure of the regression function. Studying the Gibbs posterior distr
ibution from a frequentist Bayesian perspective\, we analyze the diameter
and show high coverage probability of the resulting credible sets. The met
hod is illustrated with an animation in a simulation example.\n\nThis talk
is based on joint work with Mathias Trabs.\n\nhttps://conference2.aau.at/
event/131/contributions/1238/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1238/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Long-range voter model on the real line
DTSTART;VALUE=DATE-TIME:20220805T093000Z
DTEND;VALUE=DATE-TIME:20220805T095000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1228@conference2.aau.at
DESCRIPTION:In the voter model on $\\mathbb{Z}$ a countable number of peop
le (called voters) have two opinions\, say $0$ or $1$\, and each voter is
placed at a site of $\\mathbb{Z}$. Each person has an exponential distribu
ted clock. If the clock rings the voter adopts the opinion of a randomly c
hosen neighbour. It is well known that this process satisfies a moment dua
lity with a coalescing random walk. We are interested in a situation where
an uncountable number of voters is placed on the real line and we allow t
hat they adopt their opinion of other voters that are far away. Hence we t
hink of a measure valued process satisfying a moment duality relation with
a coalescing system of symmetric $\\alpha$-stable processes with $\\alpha
\\in (1\,2)$. Such a process has been constructed by Steven N. Evans in 1
997 where he allows more general coalescing mechanisms and infinitely many
opinions. In the talk I will introduce the process and talk about some fr
actional properties. This is joint work in progress with my supervisor Ach
im Klenke and with Leonid Mytnik.\n\nhttps://conference2.aau.at/event/131/
contributions/1228/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1228/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hegelsmann-Krause model with environmental noise
DTSTART;VALUE=DATE-TIME:20220805T090000Z
DTEND;VALUE=DATE-TIME:20220805T092000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1231@conference2.aau.at
DESCRIPTION:With the rapid development of the internet and social networks
in the last decades\, more people than ever can express and share their o
pinions. Even though everyone has access to this information\, algorithms
filter the opinions such that viewpoints\, which lie outside your core bel
iefs\, get ignored. The field of opinion dynamics describes such phenomeno
n through bounded confidence models. Based on the Hegelsmann-Krause model
introduced by Rainer Hegelsmann and Ulrich Krause in 2002 we present a tim
e continuous system of interacting particles\, which is driven by idiosync
ratic and environmental noise. In the limit we derive McKean-Vlasov equati
on. By employing a dual argument\, the Ito-Wentzell formula in combination
with reducing the time integrability via stopping time we show the existe
nce and uniqueness of the non-local\, non-linear McKean-Vlasov equation. M
oreover\, we present the propagation of chaos for the particle system by u
tilizing the associated stochastic partial differential equation.\n\nhttps
://conference2.aau.at/event/131/contributions/1231/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1231/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Epidemic Models with Partial Information: Optimal Contr
ol Problems
DTSTART;VALUE=DATE-TIME:20220805T080000Z
DTEND;VALUE=DATE-TIME:20220805T082000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1230@conference2.aau.at
DESCRIPTION:This presentation is based on and continues the companion talk
of Florent Ouabo Kamkumo. We consider stochastic optimal control problems
arising in the mathematical modeling of decision-making processes in the
cost-optimal management and containment of epidemics. We focus on the impa
ct of uncertainties such as dark figures which have been addressed in the
companion talk and can be treated as optimal control problems under partia
l information. Working with the diffusion approximations for the populatio
n dynamics and the associated Kalman filter estimates of non-observable st
ate variables leads to \n control problems for controlled diffusion proce
sses.\n This is joint work with Ralf Wunderlich\n\nhttps://conference2.aa
u.at/event/131/contributions/1230/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1230/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Epidemic Models with Partial Information : Dark Figure
and Parameters Estimation
DTSTART;VALUE=DATE-TIME:20220805T073000Z
DTEND;VALUE=DATE-TIME:20220805T075000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1232@conference2.aau.at
DESCRIPTION:Mathematical models of epidemics such as the current COVID-19
pandemics often use compartmental models dividing the population into seve
ral compartments. Based on a microscopic setting describing the temporal e
volution of the subpopulation sizes in the compartments by stochastic coun
ting processes one can derive macroscopic models for large populations des
cribing the average behavior by associated ODEs such as the celebrated SIR
model. Further\, diffusion approximations allow to address fluctuations f
rom the average and to describe the state dynamics also for smaller popula
tions by stochastic differential equations (SDE).\nUsually not all of the
state variables are directly observable and we are facing the so-called
“dark figure” problem addressing for example the unknown number of asy
mptomatic and non-detected infections. Such not directly observable states
are problematic if it comes to the computation of characteristics of the
epidemic such as the effective reproduction rate and the prevalence of the
infection within the population. Further\, the management and containment
of epidemics relying on solutions of (stochastic) optimal control problem
s and the associated feedback controls need observations of the current st
ate as input.\nThe estimation of unobservable states based on records of t
he observable states leads to a non-standard filtering problem for observa
ble stochastic models. We adopt the extended Kalman filter approach coping
with non-linearities in the state dynamics and the state-dependent diffus
ion coefficients in the SDEs. This allows to develop approximative solutio
ns to that filtering problem.\nThe proposed model depends on a variety of
parameters that can be time-dependent and have been calibrated to real-wor
ld data for COVID-19. There\, we apply maximum-likelihood and Kalman filte
r methods. We illustrate our theoretical finding by numerical results.\n\n
https://conference2.aau.at/event/131/contributions/1232/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1232/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adaptive MCMC for doubly intractable distributions
DTSTART;VALUE=DATE-TIME:20220805T070000Z
DTEND;VALUE=DATE-TIME:20220805T072000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1229@conference2.aau.at
DESCRIPTION:Bayesian inference in the context of biophysical problems may
lead to posterior densities with two unknown quantities\, the normalizing
constant and \nan intractable multiplicative factor in the likelihood func
tion. \nNot being able to evaluate the likelihood function leads to comput
ational issues in classical (adaptive) MCMC algorithms and in the past yea
rs various methods have been suggested to overcome this problem. \nWe disc
uss an adaptive MCMC scheme that relies on approximating the likelihood fu
nction and\, \nmoreover\, we present a strong law of large numbers for mou
nded measurable functions.\n\nhttps://conference2.aau.at/event/131/contrib
utions/1229/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1229/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Multiplicative deconvolution under unknown error distribution
DTSTART;VALUE=DATE-TIME:20220804T140000Z
DTEND;VALUE=DATE-TIME:20220804T142000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1217@conference2.aau.at
DESCRIPTION:In this talk\, we construct a nonparametric estimator of the d
ensity $f:\\mathbb R_+ \\rightarrow \\mathbb R_+$ of a positive random var
iable $X$ based on an i.i.d. sample $(Y_1\, \\dots\, Y_n)$ of\n\\begin{equ
ation}Y=X\\cdot U\,\n\\end{equation} where $U$ is a second positive random
variable independent of $X$. More precisely\, we consider the case where
the distribution of $U$ is unknown but an i.i.d. sample $(\\widetilde U_1\
, \\dots\, \\widetilde U_m)$ of the error random variable $U$ is given. \n
Based on the estimation of the Mellin transforms of $Y$ and $U$\, and a sp
ectral cut-off regularisation of the inverse Mellin transform\, we propose
a fully data-driven density estimator where the choice of the spectral cu
t-off parameter is dealt by a model selection approach. We demonstrate the
reasonable performance of our estimator using a Monte-Carlo simulation.\n
\nhttps://conference2.aau.at/event/131/contributions/1217/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1217/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Measuring statistical dependency with optimal transport
DTSTART;VALUE=DATE-TIME:20220804T133000Z
DTEND;VALUE=DATE-TIME:20220804T135000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1222@conference2.aau.at
DESCRIPTION:In this talk\, we introduce a novel framework for measuring st
atistical dependency between two random variables $X$ and $Y$\, the *trans
port dependency* $\\tau(X\, Y) \\ge 0$. This coefficient relies on the not
ion of optimal transport and is applicable to random variables\, taking va
lues in general Polish spaces. It can be estimated consistently via the co
rresponding empirical measure\, is versatile and adaptable to various scen
arios by proper choices of the cost function\, and intrinsically respects
metric properties of the ground spaces. Notably\, statistical independence
is characterized by $\\tau(X\, Y) = 0$\, while large values of $\\tau(X\,
Y)$ indicate highly regular relations between $X$ and $Y$. Indeed\, for s
uitable base costs\, $\\tau(X\, Y)$ is maximized if and only if $Y$ can be
expressed as 1-Lipschitz function of $X$ or vice versa.\nWe exploit this
characterization and define a class of dependency coefficients with values
in $[0\, 1]$\, which can emphasizes different functional relations. In p
articular\, for suitable costs the *transport correlations* is symmetric a
nd attains the value $1$ if and only if $Y = f(X)$ where $f$ is a multiple
of an isometry\, which makes it comparable to the distance correlation.\n
Finally we illustrate how the transport dependency can be used in practice
to explore dependencies between random variables\, in a gene expression s
tudy.\n\nhttps://conference2.aau.at/event/131/contributions/1222/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1222/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Signal Processing with Gabor Frames: Variational Problems\, Compre
ssion\, and Noise Removal
DTSTART;VALUE=DATE-TIME:20220804T123000Z
DTEND;VALUE=DATE-TIME:20220804T125000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1225@conference2.aau.at
DESCRIPTION:We present solutions for variational problems\, compression an
d noise removal using gabor frames. For an appropriate window function\, a
signal $ f \\in \\mathcal{L}^2(\\mathbb{R}^d)$ possesses a non-orthogona
l gabor frames expansions in terms of the dual frames with unconditional c
onvergence in $ \\mathcal{L}^2(\\mathcal(R)^d) $. We derive approximate mi
nimizers of variational problems and compression in modulation spaces. Wit
hin the Gaussian white noise model we provide minimax bounds for rates of
convergence over modulation spaces using soft-thresholding of the Gabor co
efficients. Numerical experiments complement the theoretical results. Furt
hermore we extend our results onto $\\alpha$-modulation spaces\, providing
a flexible Gabor-wavelet transform of signals.\n\nhttps://conference2.aau
.at/event/131/contributions/1225/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1225/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Extrema of high dimensional data
DTSTART;VALUE=DATE-TIME:20220804T120000Z
DTEND;VALUE=DATE-TIME:20220804T122000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1218@conference2.aau.at
DESCRIPTION:In this talk we present a method to determine the directions
of multivariate extremes. Therefore the concept of sparse regular variatio
n of Meyer and Wintenberger (2021b) is introduced. In contrast to regular
variation the limit measure in the definition of sparse regular variation
is more sparse. The limit measure is called spectral measure and models th
e dependence in extremes. Sparse regular variation is based on an Euclide
an projection onto the simplex and allows the categorization of extremes w
ith respect to the cones of the simplex. The support of the spectral measu
re is determined by finding components in the data which are very large\,
while all other components are small. This is done by categorization of ex
tremes to cones of the simplex and fitting a multinomial model to the numb
er of extremes in the different cones (Meyer and Wintenberger (2021a)). Fo
r estimating the number of extremal cones we derive some information crite
ria\, e.g. AIC (Meyer and Wintenberger (2021a)).\n\nReferences:\nMeyer\, N
. and O. Wintenberger (2021a). "Multivariate sparse clustering for extreme
s". In: arXiv: 2007.11848 [math.ST].\n\nMeyer\, N. and O. Wintenberger (20
21b). "Sparse regular variation". In: Advances in Applied Probability 53(4
)\, pp. 1115-1148.\n\nhttps://conference2.aau.at/event/131/contributions/1
218/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1218/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Causal Interventions to Reduce the Risk of Adverse Events in Stent
Procedures
DTSTART;VALUE=DATE-TIME:20220804T113000Z
DTEND;VALUE=DATE-TIME:20220804T115000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1223@conference2.aau.at
DESCRIPTION:The main medical intervention for coronary artery disease is s
tent implantation. In this context\, we statistically estimate causal eff
ects of alternate treatment regimes with the aim to lower the risk of adve
rse events as e.g. heart attacks. For this\, a causal DAG is designed by d
omain experts and refined by a causal discovery algorithm. The estimated g
raph allows for appropriate confounder adjustment in the associated graphi
cal model. We show how to non-parametrically compute average effects of ca
usal interventions on continuous treatment variables and propose a heurist
ic to find explainable treatment regimes decreasing the risk of adverse ev
ents. The results give directions to improve upon and thus reduce the spac
e of costly\, future medical studies.\n\nhttps://conference2.aau.at/event/
131/contributions/1223/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1223/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Identification in Graphical Continuous Lyapunov Models
DTSTART;VALUE=DATE-TIME:20220804T080000Z
DTEND;VALUE=DATE-TIME:20220804T082000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1215@conference2.aau.at
DESCRIPTION:Graphical continuous Lyapunov models offer a new perspective o
n modeling the causally interpretable dependence structure in multivariate
data by treating each independent observation as a one-time cross-section
al snapshot of the multivariate Ornstein-Uhlenbeck process in equilibrium.
This leads to Gaussian models in which the covariance matrix is determine
d by the continuous Lyapunov equation. In this setting\, each graphical mo
del assumes a sparse drift matrix with support determined by a directed gr
aph. We study the crucial problem of parameter identifiability in the clas
s of graphical continuous Lyapunov models. Indeed\, given a statistical mo
del induced by a graph\, it is essential for statistical analysis to clari
fy if it is possible to uniquely recover the parameters from the joint dis
tribution of the observed variables.\n\nWe show that this question can be
reduced to analyzing the rank of certain sparse matrices with covariances
as entries. Depending on the graph under consideration\, the structure of
these matrices changes in subtle ways. We study the identifiability for di
fferent classes of graphs. In our main result we prove that global identif
iability holds if and only if the graph is simple (i.e.\, contains at most
one edge between any two nodes). Furthermore\, we present intriguing exam
ples of non-simple graphs for which the associated model has generically i
dentifiable parameters.\n\nhttps://conference2.aau.at/event/131/contributi
ons/1215/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1215/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conditional predictive inference for linear sub-models of high-dim
ensional data
DTSTART;VALUE=DATE-TIME:20220804T073000Z
DTEND;VALUE=DATE-TIME:20220804T075000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1216@conference2.aau.at
DESCRIPTION:We deal with the estimation of the distribution of the predict
ion error conditional on the training data based on a jackknife type appro
ach in a setting where the number of regressors grows proportionally with
the number of observations. That estimation may be used to construct (asym
ptotically valid) confidence intervals as well as estimating the MSE ore M
AE of the method used in the prediction. While both the true and the worki
ng model are restricted to be linear\, we allow for a misspecified setting
in the sense that only a lower-dimensional linear transformation of the t
rue regressors are available. We show that for a range of estimators inclu
ding the OLS estimator our approach leads to an asymptotically accurate es
timation.\n\nhttps://conference2.aau.at/event/131/contributions/1216/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1216/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Regression estimation via best L_2-approximation on spaces of step
functions with two jumps
DTSTART;VALUE=DATE-TIME:20220804T070000Z
DTEND;VALUE=DATE-TIME:20220804T072000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1224@conference2.aau.at
DESCRIPTION:In general regression models the equation $Y = m(X) + \\epsilo
n$ holds\, where $X\,Y$ and $\\epsilon$ are random variables\, $m(X) = \\m
athbb{E}[Y \\vert X]$ and the regression function $m$ is unknown.\nThe app
roach by Nadine Albrecht\, 2020\, uses step functions with one jump\, e.g.
binary decision trees\, as an approximation of $m$ in $L_2$ and assumes t
he unique existence of optimal step function parameters for the approximat
ion. With given independent\, identically distributed samples $(X_i\,Y_i)_
{i \\in \\mathbb{N}}$ it is possible to formulate the empirical equivalent
of the approximation via step functions. As a consequence stochastic proc
esses appear in the multivariate Skorokhod space $D(\\mathbb{R}^d)$. \nOur
research interest is the extension to multiple step functions with arbitr
ary\, finite jumps. Under certain conditions first results\, similarly to
the case with one jump\, are examined for step functions with two jumps\,
including stochastic boundedness\, convergence in distribution of the empi
rical processes and consistency of the estimators. By the usage of the Arg
inf theorems introduced by Dietmar Ferger\, 2015\, confidence regions for
the parameters in the step functions can be constructed.\n\nhttps://confer
ence2.aau.at/event/131/contributions/1224/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1224/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Central Limit Theorem for Centered Purely Random Forests using U
-Statistic Theory
DTSTART;VALUE=DATE-TIME:20220803T160000Z
DTEND;VALUE=DATE-TIME:20220803T162000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1220@conference2.aau.at
DESCRIPTION:Random forests are a popular method in supervised learning and
can be\nused for regression and classification problems. For a regression
problem\na random forest averages the results of several randomized decis
ion trees\nthat are constructed on different subsamples of the dataset. In
practice\nrandom forests appear to be very successful and are therefore a
commonly\nused algorithm. Contrary to this there is little known about th
e\nmathematical properties of classic random forests that use data depende
nt\npartitions. Most results in the literature cover simpler versions of r
andom\nforests often with partitions that are independent of the dataset.
One\nexample of these simpler algorithms are centered purely random forest
s.\nMoreover the majority of the results in the literature are consistency
theorems\nand there are noticeably less central limit theorems. In our wo
rk\nwe prove a central limit theorem for centered purely random forests. T
he\nproof uses results by Peng et al. (2022) which are based on an interpr
etation\nof random forests as generalized U-Statistics.\n\n**References**\
nWei Peng\, Tim Coleman\, and Lucas Mentch. Rates of convergence for rando
m\nforests via generalized u-statistics. *Electronic Journal of Statistics
*\,\n16(1):232–292\, 2022.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1220/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1220/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Using Statistics to Determine the Learning Rate for Gradient Desce
nt
DTSTART;VALUE=DATE-TIME:20220803T153000Z
DTEND;VALUE=DATE-TIME:20220803T155000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1233@conference2.aau.at
DESCRIPTION:While gradient descent is ubiquitous in Machine Learning\,
there is no adaptive way to select a learning rate yet. This forces practi
tioners to do "hyperparameter tuning". We review how optimization schemes
can be motivated using Taylor approximations and develop intuition why thi
s results in unknown hyperparameters. We then replace the Taylor approxima
tion with a statistical Best Linear Unbiased Estimator (BLUE) and derive g
radient descent again. But this time with calculable learning rates.\n\nht
tps://conference2.aau.at/event/131/contributions/1233/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1233/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Construction of Admissible Decision Procedures in Statistical Clas
sification
DTSTART;VALUE=DATE-TIME:20220803T123000Z
DTEND;VALUE=DATE-TIME:20220803T125000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1221@conference2.aau.at
DESCRIPTION:To classify an observation\, we assume that each class can be
represented by a probability distribution\, which might be the result of a
previous estimate. An older but famous example is provided by Fisher's cl
assification of iris species based on length measurements of their sepals
and petals with class-related distributions. With the increasing relevance
of machine learning methods\, classification is a current research topic.
Applications include object classification in image recognition or text c
lassification\, often referring to the example of spam filters. Although c
lassification problems arise almost everywhere in the digital world and nu
merous algorithmic solutions are being worked on\, even elementary mathema
tical foundations seem to have been treated only incompletely or for speci
al cases so far.\n\nFraming classification in terms of statistical decisio
n theory\, we consider a classification problem as a family of probability
distributions $(P_i:i \\in I)$ with a finite class index set $I$ being th
e decision space\, and investigate several optimality criteria of randomis
ed decision procedures. In this regard\, we obtained the result that a gen
eralization of the Neyman-Pearson lemma characterizes all admissible proce
dures\, that is\, procedures with minimal error probabilities. In certain
binary problems\, this characterization yields procedures representable by
class separating nonlinear hypersurfaces. Note that hyperplanes therefore
generally do not provide admissible classification\, even if the training
data should be linearly separable. The aim of this talk is to present som
e further geometrical conditions for admissibility based on the risk set\,
and to deduce an analytical method for determining admissible procedures\
, in particular those that additionally fulfill the minimax condition\, an
d to indicate further questions we intend to pursue.\n\nhttps://conference
2.aau.at/event/131/contributions/1221/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1221/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Confidence in Causal Discovery with Linear Causal Models
DTSTART;VALUE=DATE-TIME:20220803T120000Z
DTEND;VALUE=DATE-TIME:20220803T122000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1227@conference2.aau.at
DESCRIPTION:Inferring causal relations of a system is a fundamental proble
m of statistics. A widely studied approach employs structural causal model
s that model noisy functional relations among a set of interacting variabl
es. The underlying causal structure is naturally represented by a directed
graph whose edges indicate direct causal dependencies. Under the assumpti
on of linear relations with homoscedastic Gaussian errors this causal grap
h and\, thus also\, causal effects are identifiable from mere observationa
l data. Over the past decade\, two main lines of research evolved\, learni
ng the causal graph as well as estimating causal effects when the graph is
known. However\, a two-step method\, that first learns a graph and then t
reats the graph as known yields confidence intervals that are overly optim
istic and can drastically fail to account for the uncertain causal structu
re. In this talk\, I will address this issue and present a framework based
on test inversion that allows us to give confidence regions for total cau
sal effects that capture both sources of uncertainty: causal structure and
numerical size of nonzero effects.\n\nhttps://conference2.aau.at/event/13
1/contributions/1227/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1227/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Half-Trek Criterion for Identifiability of Latent Variable Models
DTSTART;VALUE=DATE-TIME:20220803T113000Z
DTEND;VALUE=DATE-TIME:20220803T115000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1219@conference2.aau.at
DESCRIPTION:Linear structural equation models relate random variables of i
nterest via a linear equation system that features stochastic noise. Each
model corresponds to a directed graph whose edges represent the non-zero c
oefficients in the equation system. Prior research has developed a variety
of methods to decide parameter identifiability in models with latent vari
ables. Identifiability holds if the coefficients associated with the edges
of the graph can be uniquely recovered from the covariance matrix they de
fine. The methods usually operate in a latent projection framework where t
he confounding effects of the latent variables are represented by correlat
ion among noise terms and this approach is effective when latent confoundi
ng is sparse. In this talk I will present a new combinatorial criterion fo
r parameter identifiability that operates on the original unprojected late
nt variable model and is able to certify identifiability in settings\, whe
re some latent variables may also have dense effects on many or even all o
f the observables.\n\nhttps://conference2.aau.at/event/131/contributions/1
219/
LOCATION:Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1219/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geodesic slice sampling on the sphere
DTSTART;VALUE=DATE-TIME:20220805T093000Z
DTEND;VALUE=DATE-TIME:20220805T095000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1202@conference2.aau.at
DESCRIPTION:We introduce a geodesic slice sampler on the Euclidean sphere
(in arbitrary but fixed dimension) that can be used for approximate sampli
ng from distributions that have a density with respect to the correspondin
g surface measure. Such distributions occur e.g. in the modelling of direc
tional data or shapes. Under some mild conditions we show that the corresp
onding transition kernel is well-defined\, in particular\, that it is reve
rsible with respect to the distribution of interest.\nMoreover\, if the de
nsity is bounded away from zero and infinity\, then we obtain a uniform er
godicity convergence result.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1202/
LOCATION: Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1202/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The maximum of branching Brownian motion
DTSTART;VALUE=DATE-TIME:20220805T090000Z
DTEND;VALUE=DATE-TIME:20220805T092000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1204@conference2.aau.at
DESCRIPTION:The order of the maximum of branching Brownian motion (BBM) di
ffers in a logarithmic correction term from the one in corresponding indep
endent setting. In this talk we zoom into this transition. We study "varia
ble speed branching Brownian motions" where the "speed functions"\, that d
escribe the time-inhomogeneous variance\, approach the one of BBM from bel
ow. We show that the logarithmic correction only depends on the initial an
d final diffusion parameters. We will see that the key to the above result
is a precise understanding of the entropic repulsion experienced by an ex
tremal particle.\nBased on joint work in progress with Lisa Hartung.\n\nht
tps://conference2.aau.at/event/131/contributions/1204/
LOCATION: Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1204/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Applying monoid duality to interacting particle systems
DTSTART;VALUE=DATE-TIME:20220805T080000Z
DTEND;VALUE=DATE-TIME:20220805T082000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1213@conference2.aau.at
DESCRIPTION:In the study of interacting particle systems duality is an imp
ortant\ntool used to prove various types of long-time behavior\, for examp
le convergence to an invariant distribution. The two most used types of du
alities\nare additive and cancellative dualities\, which we are able to tr
eat in a unified framework considering commutative monoids (i.e.\\ semigro
ups containing a neutral element) as cornerstones of such a duality. For i
nteracting particle systems on local state spaces with more than two eleme
nts this approach revealed formerly unknown dualities. \n\nAs an applicati
on of one of the newly found dualities a convergence result of a combinati
on of the \\emph{contact process} and its cancellative version\, formerly
known as the \\emph{annihilating branching process}\, is presented.\n\nhtt
ps://conference2.aau.at/event/131/contributions/1213/
LOCATION: Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1213/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantifying the almost sure uniform convergence of eigenvalue-coun
ting functions
DTSTART;VALUE=DATE-TIME:20220805T073000Z
DTEND;VALUE=DATE-TIME:20220805T075000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1198@conference2.aau.at
DESCRIPTION:This talk will introduce the concept of almost-additive functi
ons on lattices with the special case of eigenvalue-counting functions of
random Schrödinger operators and showcase how they can be used in conjunc
tion with some results from empirical process theory to find explicit erro
r estimates for their convergence to the integrated density of states. Thi
s talk is based on joint work with Christoph Schumacher\, Fabian Schwarzen
berger and Ivan Veselić.\n\nhttps://conference2.aau.at/event/131/contribu
tions/1198/
LOCATION: Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1198/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Parabolic Fractal Geometry
DTSTART;VALUE=DATE-TIME:20220805T070000Z
DTEND;VALUE=DATE-TIME:20220805T072000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1210@conference2.aau.at
DESCRIPTION:The parabolic fractal geometry inheres a certain non-linear sc
aling between time and space. It is useful to determine the Hausdorff dime
nsion of self-similar stochastic processes plus deterministic drift functi
on in terms of the drift function alone. An explicit formula for the Hausd
orff dimension of isotropic stable Lévy processes plus drift will be pres
ented.\n\nhttps://conference2.aau.at/event/131/contributions/1210/
LOCATION: Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1210/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lower variance bounds for Poisson functionals
DTSTART;VALUE=DATE-TIME:20220804T140000Z
DTEND;VALUE=DATE-TIME:20220804T142000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1209@conference2.aau.at
DESCRIPTION:Lower bounds for variances are often needed to derive central
limit theorems. In this talk\, we establish a specific lower bound for the
variance of a Poisson functional that uses the difference operator of Mal
liavin calculus. \nPoisson functionals\, i.e. random variables that depend
on a Poisson process\, are widely used in stochastic geometry. In this ta
lk\, we show how to apply our lower variance bound to statistics of spatia
l random graphs\, the $L^p$ surface area of random polytopes and the volum
e of excursion sets of Poisson shot noise processes. This talk is based on
joint work with M. Schulte.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1209/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1209/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A simplified second-order Gaussian Poincaré inequality with appli
cation to random subgraph counting
DTSTART;VALUE=DATE-TIME:20220804T133000Z
DTEND;VALUE=DATE-TIME:20220804T135000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1208@conference2.aau.at
DESCRIPTION:A simplified second-order Gaussian Poincaré inequality for no
rmal approximation of functionals over infinitely many Rademacher random v
ariables is derived. It is based on a new bound for the Kolmogorov distanc
e between a general Rademacher functional and a Gaussian random variable\,
which is established by means of the discrete Malliavin-Stein method and
is of independent interest. As an application\, standardized subgraph coun
ts in the Erdős-Rényi random graph are discussed.\n\nhttps://conference2
.aau.at/event/131/contributions/1208/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1208/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Short paths in scale-free percolation
DTSTART;VALUE=DATE-TIME:20220804T123000Z
DTEND;VALUE=DATE-TIME:20220804T125000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1206@conference2.aau.at
DESCRIPTION:Graph distances in real networks\, in particular social networ
ks\, have been always in the focus of network research since Milgram's exp
eriment in 60s. In this talk we specialise in a geometric random graph kno
wn as scale-free percolation\, which shows a rich phase diagram\, and focu
s on short paths in it. In this model\, $x\,y \\in \\mathbb{Z}^d$ are conn
ected with probability depending on i.i.d weights and their Euclidean dist
ance $|x-y|$.\n\nFirst we study asymptotic distances in a regime where gra
ph distances are poly-logarithmic in Euclidean distance. With a multi-scal
e argument we obtain improved bounds on the logarithmic exponent. In the
heavy tail regime\, improvement of the upper bound shows a discrepancy wit
h the long-range percolation. In the light tail regime\, the correct expon
ent is identified.\n\nIn the following part we investigate navigation poss
ibility in the model. More precisely\, we study whether it is possible to
find the shortest paths between two vertices\, given only local informatio
n (weights and locations of neighbors). In the doubly logarithmic regime\,
a greedy routing algorithm enables us to find a comparably long path as t
he shortest one up to the prefactor.\n\nhttps://conference2.aau.at/event/1
31/contributions/1206/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1206/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Component sizes of scale-free inhomogeneous random graphs
DTSTART;VALUE=DATE-TIME:20220804T120000Z
DTEND;VALUE=DATE-TIME:20220804T122000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1214@conference2.aau.at
DESCRIPTION:The Norros-Reittu model is an inhomogeneous random multigraph
that exhibits the so-called scale-free or power-law behaviour\, which is o
bserved in real-world complex networks. We study the component sizes of th
e Norros-Reittu model in the subcritical regime\, i.e. in the abscence of
a giant component\, and show convergence of the point process of the compo
nent sizes to a Poisson process. The same result holds for closely related
graphs such as the Chung-Lu model and the generalized random graph. It is
planned to derive similar results for geometric graph models like the ran
dom connection model.\n\nhttps://conference2.aau.at/event/131/contribution
s/1214/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1214/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Random walks on graphs and the Floyd boundary
DTSTART;VALUE=DATE-TIME:20220804T113000Z
DTEND;VALUE=DATE-TIME:20220804T115000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1205@conference2.aau.at
DESCRIPTION:We consider a random walk on a graph\, in order to study its b
ehavior at infinity\, it is natural to consider a boundary for the graph.
After obtaining such a structure\, a question that arises is whether the l
imit of the random walk exists. In this talk we will define the Floyd boun
dary of a graph. Furthermore we will present some assumptions on the rando
m walk that induce convergence to the boundary.\n\nhttps://conference2.aau
.at/event/131/contributions/1205/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1205/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximum interpoint distance of high-dimensional random vectors
DTSTART;VALUE=DATE-TIME:20220804T080000Z
DTEND;VALUE=DATE-TIME:20220804T082000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1203@conference2.aau.at
DESCRIPTION:A limit theorem for the largest interpoint distance of $p$ i.i
.d. points on $\\mathbb R^n$ to the Gumbel distribution is proven\, where
the number of points $p=p_n$ tends to infinity as the dimension of the poi
nts $n$ tends to infinity. The theorem holds under moment assumptions and
corresponding assumptions on the rate of $p$. The proof is based on the Ch
en-Stein Poisson approximation method and uses the sum structure of the in
terpoint distances. Therefore\, an asymptotic distribution of a more gener
al object is derived.\n\nhttps://conference2.aau.at/event/131/contribution
s/1203/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1203/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Central limit theorems for generalized descents and generalized in
versions in finite root systems
DTSTART;VALUE=DATE-TIME:20220804T073000Z
DTEND;VALUE=DATE-TIME:20220804T075000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1207@conference2.aau.at
DESCRIPTION:We start introducing generalized descents and generalized inve
rsions in permutations as special cases of antichains and order ideals in
the root poset for permutations. We provide the variance for generalized i
nversions and use a dependency graph method to conclude a central limit th
eorem for those and for antichains. We then generalize this result to anti
chains in root posets for finite Weyl groups and to generalized inversions
for irreducible Weyl groups. \nThis is joint work with Christian Stump\,
generalising the study of d-descents by Pike and Bona.\n\nhttps://conferen
ce2.aau.at/event/131/contributions/1207/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1207/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sharp Constants in Normal an Edgeworth Approximation
DTSTART;VALUE=DATE-TIME:20220804T070000Z
DTEND;VALUE=DATE-TIME:20220804T072000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1211@conference2.aau.at
DESCRIPTION:We all know and love the central limit theorem (CLT) but there
is a lot more to wish for. The Berry-Esseen theorem overestimates the act
ual error in the CLT and truly sharp error bounds for specific distributio
ns are\, as far as we are aware\, only known in binomial cases and can be
found in Schulz (2016). Even less seems to be known for other distances an
d higher-order approximations.\n\nIn order to make progress here we consid
er it to be advisable to solve these problems for specific distributions s
uch as the binomial and the uniform distribution first. These are interest
ing in their own right and hopefully our solutions via Fourier inversion c
an be generalized to a wider set of distributions.\n\nTo give an example w
e plan to present the following two results. We found that the optimal bou
nd in the local CLT for the symmetric binomial distribution is \n\\begin{g
ather}\n \\frac{1}{2\\sqrt{2\\pi} n^{3/2}}\n\\end{gather}\nand in the g
lobal CLT with simple continuity correction it is \n\n\\begin{gather}\n 2
\\Phi\\bigg(-\\frac{3}{\\sqrt{2}}\\bigg) \\frac{1}{n}\n\\end{gather}\n\nwh
ere $\\Phi$ is the standard normal distribution function.\n\n$\\textbf{Ref
erences}$\nSchulz\, J. (2016). The Optimal Berry-Esseen Constant in the Bi
nomial Case. Dissertation\, Universität Trier. http://ubt.opus.hbz-nrw.de
/volltexte/2016/1007/.\n\nhttps://conference2.aau.at/event/131/contributio
ns/1211/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1211/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clustering financial institutions based on Wasserstein distance
DTSTART;VALUE=DATE-TIME:20220803T150000Z
DTEND;VALUE=DATE-TIME:20220803T152000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1200@conference2.aau.at
DESCRIPTION:Financial institutions submit data on their credit portfolios
to regulators. An individual institution can be identified with a distribu
tion that is representative of its respective credit portfolio. We are int
erested in finding representative clusters of financial institutions based
on the notion of Wasserstein barycenter. A particular challenge arises fr
om missing data since financial institutions are subject to different regu
latory requirements. This leads us to establish a form of the k-means clus
tering algorithm in Wasserstein space which can deal with missing coordina
tes.\n\nThis is based on joint work with Julio Backhoff and Mathias Beiglb
öck.\n\nhttps://conference2.aau.at/event/131/contributions/1200/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1200/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Wasserstein space of stochastic processes
DTSTART;VALUE=DATE-TIME:20220803T153000Z
DTEND;VALUE=DATE-TIME:20220803T155000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1201@conference2.aau.at
DESCRIPTION:Researchers from different areas have independently defined ex
tensions of the usual weak topology between laws of stochastic processes.
This includes Aldous' extended weak convergence\, Hellwig's information t
opology and convergence in adapted distribution in the sense of Hoover-Kei
sler. We show that on the set of continuous processes with canonical filtr
ation these topologies coincide and are metrized by a suitable *adapted Wa
sserstein distance* $\\mathcal{AW}$. Moreover\, we show that the resulting
topology is the weakest topology that guarantees continuity of optimal st
opping. \n\nWhile the set of processes with natural filtration is not comp
lete\, we establish that its completion is precisely the space processes w
ith filtration $\\mathrm{FP}$. We also observe that $(\\mathrm{FP}\, \\mat
hcal{AW})$ exhibts several desirable properties. Specifically\, $(\\mathrm
{FP}\, \\mathcal{AW})$ is Polish\, martingales form a closed subset and ap
proximation results like Donsker's theorem extend to $\\mathcal{AW}$.\n\nT
his talk is based on joint work with Daniel Bartl\, Mathias Beiglböck\, G
udmund Pammer and Xin Zhang.\n\nhttps://conference2.aau.at/event/131/contr
ibutions/1201/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1201/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stochastic Optimal Control of Occupational Pension Funds Under Dyn
amic Risk Constraints
DTSTART;VALUE=DATE-TIME:20220803T123000Z
DTEND;VALUE=DATE-TIME:20220803T125000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1212@conference2.aau.at
DESCRIPTION:In this presentation we consider occupational pension funds
provided by a company to its employees. A special feature of such pension
funds is that collectives of insured persons are typically smaller and be
nefit payments depend on seniority and salary of the insured.\n Therefore
\, temporal fluctuations of the composition of the collective of insured
persons w.r.t. age\, seniority and salary can not be neglected in the c
omputation of actuarial liabilities and the company's financial contribut
ions to the fund.\n We describe the stochastic dynamics for the compositio
n of the collective of insured by a discrete-time Markov-chain model. The
resulting actuarial liabilities which are functional of the Markov-chain
are approximated by a diffusion process. The latter is used to formulate
stochastic optimal control arising in the cost-optimal management of occup
ational pension funds. We focus on discrete- time problems which can be tr
eated as a Markov Decision Process (MDP). Numerical results are presented.
\n\nhttps://conference2.aau.at/event/131/contributions/1212/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1212/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Deep neural network discretization of the Wong-Zakai approximation
of stochastic differential equations
DTSTART;VALUE=DATE-TIME:20220803T120000Z
DTEND;VALUE=DATE-TIME:20220803T122000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1197@conference2.aau.at
DESCRIPTION:In recent years\, deep neural networks (DNNs) have been succes
sfully used in many computational problems including\, for example\, fraud
detection or pattern recognition. DNN algorithms have been also proven to
be enormously successful in overcoming the curse of dimensionality\, in p
articular for solving Kolmogorov-type partial differential equations in hu
ndreds of dimensions in reasonable computation time. Nothing is known unti
l now on using neural networks in connection with the so-called Wong-Zakai
method that approximates stochastic differential equations by suitable ra
ndom ordinary differential equations. We are exploring whether neural netw
orks are numerically beneficial in this context and provide an algorithm f
or that. \nThis is joint work with Andreas Neuenkirch (University of Mannh
eim) and Michaela Szölgyenyi (University of Klagenfurt).\n\nhttps://confe
rence2.aau.at/event/131/contributions/1197/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1197/
END:VEVENT
BEGIN:VEVENT
SUMMARY:An SMP-Based Algorithm for Solving the Constrained Utility Maximiz
ation Problem via Deep Learning
DTSTART;VALUE=DATE-TIME:20220803T113000Z
DTEND;VALUE=DATE-TIME:20220803T115000Z
DTSTAMP;VALUE=DATE-TIME:20240618T012617Z
UID:indico-contribution-131-1199@conference2.aau.at
DESCRIPTION:We consider the utility maximization problem under convex cons
traints with regard to theoretical results which allow the formulation of
algorithmic solvers which make use of deep learning techniques. In particu
lar for the case of random coefficients\, we prove a stochastic maximum pr
inciple (SMP) generalizing the SMP proved by Li and Zheng (2018). We use t
his SMP together with the strong duality property for defining a new algor
ithm\, which we call deep primal SMP algorithm. Numerical examples illustr
ate the effectiveness of the proposed algorithm. Moreover\, our numerical
experiments for constrained problems show that the novel deep primal SMP a
lgorithm overcomes the deep SMP algorithm's (see Davey and Zheng (2021)) w
eakness of erroneously producing the value of the corresponding unconstrai
ned problem. Furthermore\, in contrast to the deep controlled 2BSDE algori
thm from Davey and Zheng (2021)\, this algorithm is also applicable to pro
blems with path dependent coefficients. Finally\, we propose a learning pr
ocedure based on epochs\, which improved the results of our algorithm even
further. Implementing a semi-recurrent network architecture for the contr
ol process turned out to be also a valuable advancement.\n\nhttps://confer
ence2.aau.at/event/131/contributions/1199/
LOCATION:Universität Klagenfurt HS 3
URL:https://conference2.aau.at/event/131/contributions/1199/
END:VEVENT
END:VCALENDAR