Jouko Lampinen

Rao-Blackwellized particle filter for multiple target tracking

In this article we propose a new Rao-Blackwellized particle filtering based algorithm for tracking an unknown number of targets. The algorithm is based on formulating probabilistic stochastic process models for target states, data associations, and birth and death processes. The tracking of these stochastic processes is implemented using sequential Monte Carlo sampling or particle filtering, and the efficiency of the Monte Carlo sampling is improved by using Rao-Blackwellization.

Bayesian approach for neural networks—review and case studies

We give a short review on the Bayesian approach for neural network learning and demonstrate the advantages of the approach in three real applications. We discuss the Bayesian approach with emphasis on the role of prior knowledge in Bayesian models and in classical error minimization approaches. The generalization capability of a statistical model, classical or Bayesian, is ultimately based on the prior assumptions. The Bayesian approach permits propagation of uncertainty in quantities which are unknown to other assumptions in the model, which may be more generally valid or easier to guess in the problem. The case problem studied in this paper include a regression, a classification, and an inverse problem. In the most thoroughly analyzed regression problem, the best models were those with less restrictive priors. This emphasizes the major advantage of the Bayesian approach, that we are not forced to guess attributes that are unknown, such as the number of degrees of freedom in the model, non-linearity of the model with respect to each input variable, or the exact form for the distribution of the model residuals.

Bayesian model assessment and comparison using cross-validation predictive densities

In this work, we discuss practical methods for the assessment, comparison, and selection of complex hierarchical Bayesian models. A natural way to assess the goodness of the model is to estimate its future predictive capability by estimating expected utilities. Instead of just making a point estimate, it is important to obtain the distribution of the expected utility estimate because it describes the uncertainty in the estimate. The distributions of the expected utility estimates can also be used to compare models, for example, by computing the probability of one model having a better expected utility than some other model. We propose an approach using cross-validation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions. We also discuss the probabilistic assumptions made and properties of two practical cross-validation methods, importance sampling and k-fold cross-validation. As illustrative examples, we use multilayer perceptron neural networks and gaussian processes with Markov chain Monte Carlo sampling in one toy problem and two challenging real-world problems.

Discrete Neural Signatures of Basic Emotions

Categorical models of emotions posit neurally and physiologically distinct human basic emotions. We tested this assumption by using multivariate pattern analysis (MVPA) to classify brain activity patterns of 6 basic emotions (disgust, fear, happiness, sadness, anger, and surprise) in 3 experiments. Emotions were induced with short movies or mental imagery during functional magnetic resonance imaging. MVPA accurately classified emotions induced by both methods, and the classification generalized from one induction condition to another and across individuals. Brain regions contributing most to the classification accuracy included medial and inferior lateral prefrontal cortices, frontal pole, precentral and postcentral gyri, precuneus, and posterior cingulate cortex. Thus, specific neural signatures across these regions hold representations of different emotional states in multimodal fashion, independently of how the emotions are induced. Similarity of subjective experiences between emotions was associated with similarity of neural patterns for the same emotions, suggesting a direct link between activity in these brain regions and the subjective emotional experience.

Bayesian analysis of the neuromagnetic inverse problem with ℓp-norm priors

Magnetoencephalography (MEG) allows millisecond-scale non-invasive measurement of magnetic fields generated by neural currents in the brain. However, localization of the underlying current sources is ambiguous due to the so-called inverse problem. The most widely used source localization methods (i.e., minimum-norm and minimum-current estimates (MNE and MCE) and equivalent current dipole (ECD) fitting) require ad hoc determination of the cortical current distribution (l(2)-, l(1)-norm priors and point-sized dipolar, respectively). In this article, we perform a Bayesian analysis of the MEG inverse problem with l(p)-norm priors for the current sources. This way, we circumvent the arbitrary choice between l(1)- and l(2)-norm prior, which is instead rendered automatically based on the data. By obtaining numerical samples from the joint posterior probability distribution of the source current parameters and model hyperparameters (such as the l(p)-norm order p) using Markov chain Monte Carlo (MCMC) methods, we calculated the spatial inverse estimates as expectation values of the source current parameters integrated over the hyperparameters. Real MEG data and simulated (known) source currents with realistic MRI-based cortical geometry and 306-channel MEG sensor array were used. While the proposed model is sensitive to source space discretization size and computationally rather heavy, it is mathematically straightforward, thus allowing incorporation of, for instance, a priori functional magnetic resonance imaging (fMRI) information.

Hierarchical Bayesian estimates of distributed MEG sources: theoretical aspects and comparison of variational and MCMC methods

Magnetoencephalography (MEG) provides millisecond-scale temporal resolution for noninvasive mapping of human brain functions, but the problem of reconstructing the underlying source currents from the extracranial data has no unique solution. Several distributed source estimation methods based on different prior assumptions have been suggested for the resolution of this inverse problem. Recently, a hierarchical Bayesian generalization of the traditional minimum norm estimate (MNE) was proposed, in which the variance of distributed current at each cortical location is considered as a random variable and estimated from the data using the variational Bayesian (VB) framework. Here, we introduce an alternative scheme for performing Bayesian inference in the context of this hierarchical model by using Markov chain Monte Carlo (MCMC) strategies. In principle, the MCMC method is capable of numerically representing the true posterior distribution of the currents whereas the VB approach is inherently approximative. We point out some potential problems related to hyperprior selection in the previous work and study some possible solutions. A hyperprior sensitivity analysis is then performed, and the structure of the posterior distribution as revealed by the MCMC method is investigated. We show that the structure of the true posterior is rather complex with multiple modes corresponding to different possible solutions to the source reconstruction problem. We compare the results from the VB algorithm to those obtained from the MCMC simulation under different hyperparameter settings. The difficulties in using a unimodal variational distribution as a proxy for a truly multimodal distribution are also discussed. Simulated MEG data with realistic sensor and source geometries are used in performing the analyses.

Temporal Kohonen Map and the Recurrent Self-Organizing Map: Analytical and Experimental Comparison

This paper compares two Self-Organizing Map (SOM) based models for temporal sequence processing (TSP) both analytically and experimentally. These models, Temporal Kohonen Map (TKM) and Recurrent Self-Organizing Map (RSOM), incorporate leaky integrator memory to preserve the temporal context of the input signals. The learning and the convergence properties of the TKM and RSOM are studied and we show analytically that the RSOM is a significant improvement over the TKM, because the RSOM allows simple derivation of a consistent learning rule. The results of the analysis are demonstrated with experiments.

Bayesian MLP neural networks for image analysis

Abstract We demonstrate the advantages of using Bayesian multi-layer perceptron (MLP) neural networks for image analysis. The Bayesian approach provides consistent way to do inference by combining the evidence from the data to prior knowledge from the problem. A practical problem with MLPs is to select the correct complexity for the model, i.e., the right number of hidden units or correct regularization parameters. The Bayesian approach offers efficient tools for avoiding overfitting even with very complex models, and facilitates estimation of the confidence intervals of the results. In this contribution we review the Bayesian methods for MLPs and present comparison results from two case studies. In the first case, MLPs were used to solve the inverse problem in electrical impedance tomography. The Bayesian MLP provided consistently better results than other methods. In the second case, the goal was to locate trunks of trees in forest scenes. With Bayesian MLP it was possible to use large number of potentially useful features and prior for determining the relevance of the features automatically.

Time series prediction by Kalman smoother with cross-validated noise density

This article presents a classical type of solution to the time series prediction competition, the CATS benchmark, which is organized as a special session of the IJCNN 2004 conference. The solution is based on sequential application of the Kalman smoother, which is a classical statistical tool for estimation and prediction of time series. The Kalman smoother belongs to the class of linear methods, because the underlying filtering model is linear and the distributions are assumed as Gaussian. Since the time series model of the Kalman smoother assumes that the densities of noise terms are known, these are determined by cross-validation.

Stimulus-related independent component and voxel-wise analysis of human brain activity during free viewing of a feature film.

Understanding how the brain processes stimuli in a rich natural environment is a fundamental goal of neuroscience. Here, we showed a feature film to 10 healthy volunteers during functional magnetic resonance imaging (fMRI) of hemodynamic brain activity. We then annotated auditory and visual features of the motion picture to inform analysis of the hemodynamic data. The annotations were fitted to both voxel-wise data and brain network time courses extracted by independent component analysis (ICA). Auditory annotations correlated with two independent components (IC) disclosing two functional networks, one responding to variety of auditory stimulation and another responding preferentially to speech but parts of the network also responding to non-verbal communication. Visual feature annotations correlated with four ICs delineating visual areas according to their sensitivity to different visual stimulus features. In comparison, a separate voxel-wise general linear model based analysis disclosed brain areas preferentially responding to sound energy, speech, music, visual contrast edges, body motion and hand motion which largely overlapped the results revealed by ICA. Differences between the results of IC- and voxel-based analyses demonstrate that thorough analysis of voxel time courses is important for understanding the activity of specific sub-areas of the functional networks, while ICA is a valuable tool for revealing novel information about functional connectivity which need not be explained by the predefined model. Our results encourage the use of naturalistic stimuli and tasks in cognitive neuroimaging to study how the brain processes stimuli in rich natural environments.