Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 x 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present

Associative Pattern Recognition for Biological Regulation Data

In the last decade, bioinformatics data has been accumulated at an unprecedented rate, thanks to the advancement in sequencing technologies. Such rapid development poses both challenges and promising research topics. In this dissertation, we propose a series of associative pattern recognition algorithms in biological regulation studies. In particular, we emphasize efficiently recognizing associative patterns between genes, transcription factors, histone modifications and functional labels using heterogeneous data sources (numeric, sequences, time series data and textual labels). In protein-DNA associative pattern recognition, we introduce an efficient algorithm for affinity test by searching for over-represented DNA sequences using a hash function and modulo addition calculation. This substantially improves the efficiency of \textit{next generation sequencing} data analysis. In gene regulatory network inference, we propose a framework for refining weak networks based on transcription factor binding sites, thus improved the precision of predicted edges by up to 52%. In histone modification code analysis, we propose an approach to genome-wide combinatorial pattern recognition for histone code to function associative pattern recognition, and achieved improvement by up to $38.1\%$. We also propose a novel shape based modification pattern analysis approach, using this to successfully predict sub-classes of genes in flowering-time category. We also propose a combination to combination associative pattern recognition, and achieved better performance compared against multi-label classification and bidirectional associative memory methods. Our proposed approaches recognize associative patterns from different types of data efficiently, and provides a useful toolbox for biological regulation analysis. This dissertation presents a road-map to associative patterns recognition at genome wide level

Parkinsonin taudin tunnistaminen elektroenkefalogrammista koneoppimisteknologian avulla

Tässä tutkielmassa perehdytään koneoppimisteknologian käyttöön Parkinsonin tautia sairastavien ja terveiden koehenkilöiden EEG-tallenteiden erottamisessa toisistaan. EEG:n käyttö Parkinsonin taudin biomarkerina on herättänyt kiinnostusta, ja aiemmassa koneoppimisteknologiaa käyttävässä tutkimuksessa on saavutettu lupaavia tuloksia. Aiemmassa tutkimuksessa ei ole kuitenkaan tutkittu systemaattisesti EEG:n mittaamiseen käytettävien elektrodien lukumäärän vaikutusta luokittelutarkkuuteen, joka on tämän tutkielman yhteydessä toteutetun koneoppimispohjaisen EEG-analyysin ensisijainen tutkimuskysymys. Analyysin aineisto koostuu kolmella eri yliopistolla (Iowan yliopisto, New Mexicon yliopisto ja Turun yliopisto) kerätyistä, yhdistetyistä EEG-aineistoista. Aineistot on esikäsitelty PREP-esiprosessointiputken avulla, ja piirteenekstraktointiin on käytetty tyypillisten EEG-analyysin mukaisten taajuuskaistojen (delta, theta, alpha1, alpha2, beta) näyteentropia -metriikoita. Aineiston luokitteluun on käytetty logistista regressiomallia. Elektrodien lukumäärän vaikutusta mallin saavuttamaan luokittelutarkkuuteen on tutkittu käyttämällä budjetoitua ja ryhmäperustaista, ahnetta eteenpäinhakualgoritmia piirteenvalintaan. Keskeisenä havaintona huomattiin, että luokittelu onnistuu kymmenellä elektrodilla lähes yhtä hyvällä tarkkuudella (0.72) kuin käyttämällä täyttä elektrodivalikoimaa. Toissijaisesti huomattiin, että luokittelu käyttäen koehenkilöiden silmät auki mitattua EEG:tä onnistuu merkittävästi paremmin kuin käyttäen silmät kiinni mitattua EEG:tä. Lisäksi havaittiin, että elektrodien sijainnilla ei vaikuta olevan erityisen suurta merkitystä. Tämän tutkielman tulosten valossa voi olla aiheellista jatkaa tutkimuksia pienillä elektrodivalikoimilla

Interpretation of the Precision Matrix and Its Application in Estimating Sparse Brain Connectivity during Sleep Spindles from Human Electrocorticography Recordings

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an 8 x 8 electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present

The Unreasonable Effectiveness of Machine Learning in Neuroscience: Understanding High-dimensional Neural Representations with Realistic Synthetic Stimuli

Parametrizing complex natural stimuli is a difficult and long-standing challenge. We used a generative deep convergent network to represent and parametrize a large corpus of song from European starlings, a songbird species, into a compressed low-dimensional space. We applied psychophysical methods to probe categorical perception of natural starling song syllables, which reveal a shared categorical perceptual space. Some categorical boundaries are sensitive to the category assignment of training syllables, indicating that the consensus is context dependent and that underlying dimensions of the space are not independent. We record simultaneous firing from populations of 10's of neurons in a secondary auditory cortical region of anesthetized starlings. By estimating how fast population level neural representation change with respect to the stimuli, we produce a measure along a path in stimuli space that is shared between birds and descriptive of the psychophysically determined parameters in other birds. Consistent with this, we predict the behavioral psychometric function along one dimension by fitting the behavior for other dimensions to the population level neural activity. Thus, knowing how the animal responds in one sub-region of the parametrized space informs responses in other sub-regions. Our results implicate the importance of experience in shaping shared perceptual boundaries among complex communication signals and suggest the categorical representation of natural signals in secondary sensory cortices is distributed much more densely than predicted by traditional hierarchical object recognition models. This thesis also explores other applications of machine learning to solve neuroscience problems, in particular, the curse of dimensionality and exploring predictive coding and surprise. A model explicitly designed to predict future states allows the compression of high-dimensional time-varying signals into a lower-dimensional representation encoding exclusively predictive and predictable information and has many practical applications

Delay Differential Analysis of Time Series

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis

Delay Differential Analysis of Time Series

Nonlinear dynamical system analysis based on embedding theory has been used for modeling and prediction, but it also has applications to signal detection and classification of time series. An embedding creates a multidimensional geometrical object from a single time series. Traditionally either delay or derivative embeddings have been used. The delay embedding is composed of delayed versions of the signal, and the derivative embedding is composed of successive derivatives of the signal. The delay embedding has been extended to nonuniform embeddings to take multiple timescales into account. Both embeddings provide information on the underlying dynamical system without having direct access to all the system variables. Delay differential analysis is based on functional embeddings, a combination of the derivative embedding with nonuniform delay embeddings. Small delay differential equation (DDE) models that best represent relevant dynamic features of time series data are selected from a pool of candidate models for detection or classification. We show that the properties of DDEs support spectral analysis in the time domain where nonlinear correlation functions are used to detect frequencies, frequency and phase couplings, and bispectra. These can be efficiently computed with short time windows and are robust to noise. For frequency analysis, this framework is a multivariate extension of discrete Fourier transform (DFT), and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short or sparse time series and can be extended to cross-trial and cross-channel spectra if multiple short data segments of the same experiment are available. Together, this time-domain toolbox provides higher temporal resolution, increased frequency and phase coupling information, and it allows an easy and straightforward implementation of higher-order spectra across time compared with frequency-based methods such as the DFT and cross-spectral analysis