Adaptive Markov chain Monte Carlo and Bayesian filtering for state space models

This thesis is concerned with the state and parameter estimation in state space models. The estimation of states and parameters is an important task when mathematical modeling is applied to many different application areas such as the global positioning systems, target tracking, navigation, brain imaging, spread of infectious diseases, biological processes, telecommunications, audio signal processing, stochastic optimal control, machine learning, and physical systems. In Bayesian settings, the estimation of states or parameters amounts to computation of the posterior probability density function. Except for a very restricted number of models, it is impossible to compute this density function in a closed form. Hence, we need approximation methods. A state estimation problem involves estimating the states (latent variables) that are not directly observed in the output of the system. In this thesis, we use the Kalman filter, extended Kalman filter, Gauss–Hermite filters, and particle filters to estimate the states based on available measurements. Among these filters, particle filters are numerical methods for approximating the filtering distributions of non-linear non-Gaussian state space models via Monte Carlo. The performance of a particle filter heavily depends on the chosen importance distribution. For instance, inappropriate choice of the importance distribution can lead to the failure of convergence of the particle filter algorithm. In this thesis, we analyze the theoretical Lᵖ particle filter convergence with general importance distributions, where p ≥2 is an integer. A parameter estimation problem is considered with inferring the model parameters from measurements. For high-dimensional complex models, estimation of parameters can be done by Markov chain Monte Carlo (MCMC) methods. In its operation, the MCMC method requires the unnormalized posterior distribution of the parameters and a proposal distribution. In this thesis, we show how the posterior density function of the parameters of a state space model can be computed by filtering based methods, where the states are integrated out. This type of computation is then applied to estimate parameters of stochastic differential equations. Furthermore, we compute the partial derivatives of the log-posterior density function and use the hybrid Monte Carlo and scaled conjugate gradient methods to infer the parameters of stochastic differential equations. The computational efficiency of MCMC methods is highly depend on the chosen proposal distribution. A commonly used proposal distribution is Gaussian. In this kind of proposal, the covariance matrix must be well tuned. To tune it, adaptive MCMC methods can be used. In this thesis, we propose a new way of updating the covariance matrix using the variational Bayesian adaptive Kalman filter algorithm.

Deep generative models for facial keypoints detection

A new area of machine learning research called deep learning, has moved machine learning closer to one of its original goals: artificial intelligence and general learning algorithm. The key idea is to pretrain models in completely unsupervised way and finally they can be fine-tuned for the task at hand using supervised learning. In this thesis, a general introduction to deep learning models and algorithms are given and these methods are applied to facial keypoints detection. The task is to predict the positions of 15 keypoints on grayscale face images. Each predicted keypoint is specified by an (x,y) real-valued pair in the space of pixel indices. In experiments, we pretrained deep belief networks (DBN) and finally performed a discriminative fine-tuning. We varied the depth and size of an architecture. We tested both deterministic and sampled hidden activations and the effect of additional unlabeled data on pretraining. The experimental results show that our model provides better results than publicly available benchmarks for the dataset.

Sentence Compression with Supervised Machine Learning

The subject of the thesis is automatic sentence compression with machine learning, so that the compressed sentences remain both grammatical and retain their essential meaning. There are multiple possible uses for the compression of natural language sentences. In this thesis the focus is generation of television program subtitles, which often are compressed version of the original script of the program. The main part of the thesis consists of machine learning experiments for automatic sentence compression using different approaches to the problem. The machine learning methods used for this work are linear-chain conditional random fields and support vector machines. Also we take a look which automatic text analysis methods provide useful features for the task. The data used for machine learning is supplied by Lingsoft Inc. and consists of subtitles in both compressed an uncompressed form. The models are compared to a baseline system and comparisons are made both automatically and also using human evaluation, because of the potentially subjective nature of the output. The best result is achieved using a CRF - sequence classification using a rich feature set. All text analysis methods help classification and most useful method is morphological analysis. Tutkielman aihe on suomenkielisten lauseiden automaattinen tiivistäminen koneellisesti, niin että lyhennetyt lauseet säilyttävät olennaisen informaationsa ja pysyvät kieliopillisina. Luonnollisen kielen lauseiden tiivistämiselle on monta käyttötarkoitusta, mutta tässä tutkielmassa aihetta lähestytään television ohjelmien tekstittämisen kautta, johon käytännössä kuuluu alkuperäisen tekstin lyhentäminen televisioruudulle paremmin sopivaksi. Tutkielmassa kokeillaan erilaisia koneoppimismenetelmiä tekstin automaatiseen lyhentämiseen ja tarkastellaan miten hyvin erilaiset luonnollisen kielen analyysimenetelmät tuottavat informaatiota, joka auttaa näitä menetelmiä lyhentämään lauseita. Lisäksi tarkastellaan minkälainen lähestymistapa tuottaa parhaan lopputuloksen. Käytetyt koneoppimismenetelmät ovat tukivektorikone ja lineaarisen sekvenssin mallinen CRF. Koneoppimisen tukena käytetään tekstityksiä niiden eri käsittelyvaiheissa, jotka on saatu Lingsoft OY:ltä. Luotuja malleja vertaillaan Lopulta mallien lopputuloksia evaluoidaan automaattisesti ja koska teksti lopputuksena on jossain määrin subjektiivinen myös ihmisarviointiin perustuen. Vertailukohtana toimii kirjallisuudesta poimittu menetelmä. Tutkielman tuloksena paras lopputulos saadaan aikaan käyttäen CRF sekvenssi-luokittelijaa laajalla piirrejoukolla. Kaikki kokeillut teksin analyysimenetelmät auttavat luokittelussa, joista tärkeimmän panoksen antaa morfologinen analyysi.