Conditional convex orders and measurable martingale couplings

Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp.\ increasing convex) stochastic order if and only if they admit a martingale (resp.\ submartingale) coupling. By analyzing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for real-valued random variables conditioned on a random element taking values in a general measurable space. We also provide an analogue of the conditional martingale coupling theorem in the language of probability kernels and illustrate how this result can be applied in the analysis of pseudo-marginal Markov chain Monte Carlo algorithms. We also illustrate how our results imply the existence of a measurable minimiser in the context of martingale optimal transport.Comment: 21 page

Stabilization of an overloaded queueing network using measurement-based admission control

Admission control can be employed to avoid congestion in queueing networks subject to overload. In distributed networks the admission decisions are often based on imperfect measurements on the network state. This paper studies how the lack of complete state information affects the system performance by considering a simple network model for distributed admission control. The stability region of the network is characterized and it is shown how feedback signaling makes the system very sensitive to its parameters.Comment: Published at http://dx.doi.org/10.1239/jap/1143936256 in the Journal of Applied Probability (http://projecteuclid.org/jap) by the Applied Probability Trust (http://www.appliedprobability.org/

Comparison and scaling methods for performance analysis of stochastic networks

Stochastic networks are mathematical models for traffic flows in networks with uncertainty. The goal of this thesis is to develop new methods for analyzing performance and stability of stochastic networks, helping to better understand and control uncertainty in complex distributed systems. The thesis considers three instances of stochastic networks, each representing a specific challenge for analytical modeling. The first case studies the impact of incomplete information to a queueing network with distributed admission control. Stability conditions for various admission policies are derived, together with a numerical algorithm for performance evaluation. In the second case, stochastic comparison is used to derive performance bounds for multiclass loss networks with overflow routing. The third model is a spatial random field generated by a large number of noninteracting sources, for which scaling and renormalization are used to show how the level of randomness of the individual sources may critically affect the macroscopic statistical properties of the field. The results of the thesis illustrate the feasibility of stochastic comparison and stochastic analysis in deriving approximations and performance bounds for complex physical networks with uncertainty. Approximations and performance bounds based on exact mathematical methods have the advantage that they explicitly state the type of circumstances required for the accuracy of the estimates. The resulting analytical formulas can sometimes reveal interesting properties that are not easily detected using numerical simulation.reviewe

Acute myeloid leukemia risk group prediction from gene expression data with feed-forward neural networks

Abstract. Predicting from gene expression data remains a complex task due to it characteristically having large dimensionality and small sample sizes. Creating classifiers in these settings is a non-trivial task, which is complicated by the presence of multi-class imbalance. The imbalance hinders the feed-forward neural network’s ability to learn patterns from the data, and the multi-class structure makes common evaluation metrics hide the network’s poor performance in the minority classes. For Acute Myeloid Leukemia (AML) these issues are magnified by the fact that the underlying molecular factors are heterogeneous from patient to patient, which makes treatment and prognosis difficult. Having limited resources has a direct impact on which methods can be used to tackle these problems. In this thesis, the goal is to find cost-effective methods to balance the data, remove unnecessary features and to create a multi-class classifier for AML risk group. The risk group is created using two variables based on survival times. In total six scenarios are compared for creating the optimal feed-forward neural network. First, the original gene expressions are used as the predictors without any pre-processing. The following two scenarios fix the class imbalance using SMOTE and ADASYN. Finally, RFE is used to reduce dimensions in all previous scenarios to get the last three data sets. The feed-forward neural network is tuned separately for each scenario. In total 100 parameter combinations are chosen randomly from around 3000 possible model configurations, and the resulting models are evaluated based on overall accuracy and F1 score for each class. The results show that while ADASYN, SMOTE, and RFE help the networks yield better results, having the right network structure is just as important. This is demonstrated by the fact that some models using the unprocessed data set were found among the best-performing models. Furthermore, based on high accuracy in classification, predicting the new AML risk category based only on genes seems possible even with limited resources.Akuutin myelooisen leukemian riskiryhmän ennustaminen geeniekpressiodatasta eteenpäinsyöttävillä neuroverkoilla. Tiivistelmä. Geeniekpressiodatalle on tyypillistä, että muuttujia on kerätty kymmeniä tuhansia, kun taas havaintoja on vain muutama sata. Tämän takia luokkien ennustaminen geeniekpressioista on monimutkainen tehtävä, jota vaikeuttaa epätasapaino enemmistö- ja vähemmistöluokkien välillä. Epätasapaino vaikeuttaa geenien välisten yhteyksien oppimista, ja kun luokkia on useampi, yleisesti käytetyt arviointimenetelmät piilottavat huonon luokittelukyvyn vähemmistöluokille. Näiden ongelmien lisäksi akuutti myelooinen leukemia (AML) tuo omat haasteensa potilaiden välillä olevien molekyylisten tekijöiden heterogeenisyyden vuoksi. Tämän seurauksena ennusteiden tekeminen ja hoitokeinojen suunnittelu geenien pohjalta on haastavaa. Menetelmien valitseminen edellä mainittujen ongelmien ratkaisemiseksi riippuu suoraan käytettävissä olevista resursseista. Tämän työn tavoite on löytää kustannustehokkaat menetelmät datan epätasapainon korjaamiseen ja ylimääräisten muuttujien poistamiseen, sekä luoda useamman luokan luokittelija uudelle AML riskiryhmälle. Uusi riskiryhmä luodaan kahdesta muusta muuttujasta selviytymisaikojen perusteella. Yhteensä kuutta eri tilannetta tarkastellaan eteenpäinsyöttävillä neuroverkoilla. Ensin alkuperäistä AML geeniekspressiodataa käytetään ennustamaan riskiryhmä ilman aineiston esikäsittelyä. Tämän jälkeen aineiston epätasapaino korjataan simuloimalla vähemmistöluokalle uusia havaintoja käyttäen SMOTE- ja ADASYN-algoritmeja. Viimeiset kolme aineistoa saadaan pudottamalla muuttujia edellisistä aineistoista RFE-algoritmia hyödyntäen. Eteenpäinsyöttävien neuroverkkojen optimaaliset hyperparametrien arvot haetaan 100:sta parmetrikombinaatiosta, jotka on valittu satunnaisesti noin 3000:n kombinaation ryhmästä. Valittujen neuroverkkojen tuloksia verrataan kokonaistarkkuuden, sekä jokaisesta ryhmästä erikseen saatavan F1-suureen perusteella. Parhaimpien mallien joukosta löytyi esikäsiteltyjen aineistojen lisäksi prosessoimattomia aineistoja, mikä viittaa siihen, että neuroverkkojen oikean rakenteen valitseminen on yhtä tärkeää kuin datan esikäsittely. Uuden riskiryhmän luokittelu antoi lupaavia tuloksia, joten ennustaminen pelkästään geenien pohjalta näyttäisi olevan mahdollista myös vähäisillä resursseilla

Opening minds for the wisdom of art: Encounters between art and esotericism

A reflection on the symposium ‘Clear-sighted Art – Open Mind? Encounters between Art and Esotericism’ arranged at the Amos Rex Art Museum, Helsinki, 25th August 2020