Revisiting the importance of model fitting for model-based fMRI: It does matter in computational psychiatry

Computational modeling has been applied for data analysis in psychology, neuroscience, and psychiatry. One of its important uses is to infer the latent variables underlying behavior by which researchers can evaluate corresponding neural, physiological, or behavioral measures. This feature is especially crucial for computational psychiatry, in which altered computational processes underlying mental disorders are of interest. For instance, several studies employing model-based fMRI—a method for identifying brain regions correlated with latent variables—have shown that patients with mental disorders (e.g., depression) exhibit diminished neural responses to reward prediction errors (RPEs), which are the differences between experienced and predicted rewards. Such model-based analysis has the drawback that the parameter estimates and inference of latent variables are not necessarily correct—rather, they usually contain some errors. A previous study theoretically and empirically showed that the error in model-fitting does not necessarily cause a serious error in model-based fMRI. However, the study did not deal with certain situations relevant to psychiatry, such as group comparisons between patients and healthy controls. We developed a theoretical framework to explore such situations. We demonstrate that the parameter-misspecification can critically affect the results of group comparison. We demonstrate that even if the RPE response in patients is completely intact, a spurious difference to healthy controls is observable. Such a situation occurs when the ground-truth learning rate differs between groups but a common learning rate is used, as per previous studies. Furthermore, even if the parameters are appropriately fitted to individual participants, spurious group differences in RPE responses are observable when the model lacks a component that differs between groups. These results highlight the importance of appropriate model-fitting and the need for caution when interpreting the results of model-based fMRI.     

Is Model Fitting Necessary for Model-Based fMRI?

Model-based analysis of fMRI data is an important tool for investigating the computational role of different brain regions. With this method, theoretical models of behavior can be leveraged to find the brain structures underlying variables from specific algorithms, such as prediction errors in reinforcement learning. One potential weakness with this approach is that models often have free parameters and thus the results of the analysis may depend on how these free parameters are set. In this work we asked whether this hypothetical weakness is a problem in practice. We first developed general closed-form expressions for the relationship between results of fMRI analyses using different regressors, e.g., one corresponding to the true process underlying the measured data and one a model-derived approximation of the true generative regressor. Then, as a specific test case, we examined the sensitivity of model-based fMRI to the learning rate parameter in reinforcement learning, both in theory and in two previously-published datasets. We found that even gross errors in the learning rate lead to only minute changes in the neural results. Our findings thus suggest that precise model fitting is not always necessary for model-based fMRI. They also highlight the difficulty in using fMRI data for arbitrating between different models or model parameters. While these specific results pertain only to the effect of learning rate in simple reinforcement learning models, we provide a template for testing for effects of different parameters in other models.     

Improved model-based, platform-independent feature extraction for mass spectrometry

MOTIVATION: Mass spectrometry (MS) is increasingly being used for biomedical research. The typical analysis of MS data consists of several steps. Feature extraction is a crucial step since subsequent analyses are performed only on the detected features. Current methodologies applied to low-resolution MS, in which features are peaks or wavelet functions, are parameter-sensitive and inaccurate in the sense that peaks and wavelet functions do not directly correspond to the underlying molecules under observation. In high-resolution MS, the model-based approach is more appealing as it can provide a better representation of the MS signals by incorporating information about peak shapes and isotopic distributions. Current model-based techniques are computationally expensive; various algorithms have been proposed to improve the computational efficiency of this paradigm. However, these methods cannot deal well with overlapping features, especially when they are merged to create one broad peak. In addition, no method has been proven to perform well across different MS platforms. RESULTS: We suggest a new model-based approach to feature extraction in which spectra are decomposed into a mixture of distributions derived from peptide models. By incorporating kernel-based smoothing and perceptual similarity for matching distributions, our statistical framework improves existing methodologies in terms of computational efficiency and the accuracy of the results. Our model is parameterized by physical properties and is therefore applicable to different MS instruments and settings. We validate our approach on simulated data, and show that the performance is higher than commonly used tools on real high- and low-resolution MS, and MS/MS data sets.     

Cell population dynamics model for deconvolution of murine embryonic stem cell self-renewal and differentiation responses to cytokines and extracellular matrix

Stem cell self-renewal versus differentiation fate decisions are difficult to characterize and analyze due to multiple competing rate processes occurring simultaneously among heterogeneous cell subpopulations. To address this challenge, we describe a mathematical model for cell population dynamics that allows flow cytometry measurement of population distributions of molecular markers to be deconvoluted in terms of subpopulation-specific rate parameters distinguishing commitment to differentiation, proliferation of differentiated cells, and proliferation of undifferentiated cells (i.e., self-renewal). We validate this model-based parameter determination by means of dedicated, independent cell-tracking studies. Our approach facilitates interpretation of relationships underlying effects of external cues on cell responses in differentiating cultures via intracellular signals.     

Steady state analysis of influx and transbilayer distribution of ergosterol in the yeast plasma membrane

Mathematical modeling is now frequently used in outbreak investigations to understand underlying mechanisms of infectious disease dynamics, assess patterns in epidemiological data, and forecast the trajectory of epidemics. However, the successful application of mathematical models to guide public health interventions lies in the ability to reliably estimate model parameters and their corresponding uncertainty. Here, we present and illustrate a simple computational method for assessing parameter identifiability in compartmental epidemic models. We describe a parametric bootstrap approach to generate simulated data from dynamical systems to quantify parameter uncertainty and identifiability. We calculate confidence intervals and mean squared error of estimated parameter distributions to assess parameter identifiability. To demonstrate this approach, we begin with a low-complexity SEIR model and work through examples of increasingly more complex compartmental models that correspond with applications to pandemic influenza, Ebola, and Zika. Overall, parameter identifiability issues are more likely to arise with more complex models (based on number of equations/states and parameters). As the number of parameters being jointly estimated increases, the uncertainty surrounding estimated parameters tends to increase, on average, as well. We found that, in most cases, R0 is often robust to parameter identifiability issues affecting individual parameters in the model. Despite large confidence intervals and higher mean squared error of other individual model parameters, R0 can still be estimated with precision and accuracy. Because public health policies can be influenced by results of mathematical modeling studies, it is important to conduct parameter identifiability analyses prior to fitting the models to available data and to report parameter estimates with quantified uncertainty. The method described is helpful in these regards and enhances the essential toolkit for conducting model-based inferences using compartmental dynamic models.     

BAIAP2 Is Related to Emotional Modulation of Human Memory Strength

Memory performance is the result of many distinct mental processes, such as memory encoding, forgetting, and modulation of memory strength by emotional arousal. These processes, which are subserved by partly distinct molecular profiles, are not always amenable to direct observation. Therefore, computational models can be used to make inferences about specific mental processes and to study their genetic underpinnings. Here we combined a computational model-based analysis of memory-related processes with high density genetic information derived from a genome-wide study in healthy young adults. After identifying the best-fitting model for a verbal memory task and estimating the best-fitting individual cognitive parameters, we found a common variant in the gene encoding the brain-specific angiogenesis inhibitor 1-associated protein 2 (BAIAP2) that was related to the model parameter reflecting modulation of verbal memory strength by negative valence. We also observed an association between the same genetic variant and a similar emotional modulation phenotype in a different population performing a picture memory task. Furthermore, using functional neuroimaging we found robust genotype-dependent differences in activity of the parahippocampal cortex that were specifically related to successful memory encoding of negative versus neutral information. Finally, we analyzed cortical gene expression data of 193 deceased subjects and detected significant BAIAP2 genotype-dependent differences in BAIAP2 mRNA levels. Our findings suggest that model-based dissociation of specific cognitive parameters can improve the understanding of genetic underpinnings of human learning and memory.     

Evolutionary Connectionism: Algorithmic Principles Underlying the Evolution of Biological Organisation in Evo-Devo,Evo-Eco and Evolutionary Transitions

The mechanisms of variation, selection and inheritance, on which evolution by natural selection depends, are not fixed over evolutionary time. Current evolutionary biology is increasingly focussed on understanding how the evolution of developmental organisations modifies the distribution of phenotypic variation, the evolution of ecological relationships modifies the selective environment, and the evolution of reproductive relationships modifies the heritability of the evolutionary unit. The major transitions in evolution, in particular, involve radical changes in developmental, ecological and reproductive organisations that instantiate variation, selection and inheritance at a higher level of biological organisation. However, current evolutionary theory is poorly equipped to describe how these organisations change over evolutionary time and especially how that results in adaptive complexes at successive scales of organisation (the key problem is that evolution is self-referential, i.e. the products of evolution change the parameters of the evolutionary process). Here we first reinterpret the central open questions in these domains from a perspective that emphasises the common underlying themes. We then synthesise the findings from a developing body of work that is building a new theoretical approach to these questions by converting well-understood theory and results from models of cognitive learning. Specifically, connectionist models of memory and learning demonstrate how simple incremental mechanisms, adjusting the relationships between individually-simple components, can produce organisations that exhibit complex system-level behaviours and improve the adaptive capabilities of the system. We use the term “evolutionary connectionism” to recognise that, by functionally equivalent processes, natural selection acting on the relationships within and between evolutionary entities can result in organisations that produce complex system-level behaviours in evolutionary systems and modify the adaptive capabilities of natural selection over time. We review the evidence supporting the functional equivalences between the domains of learning and of evolution, and discuss the potential for this to resolve conceptual problems in our understanding of the evolution of developmental, ecological and reproductive organisations and, in particular, the major evolutionary transitions.     

Distributional Learning of Appearance

Opportunities for associationist learning of word meaning, where a word is heard or read contemperaneously with information being available on its meaning, are considered too infrequent to account for the rate of language acquisition in children. It has been suggested that additional learning could occur in a distributional mode, where information is gleaned from the distributional statistics (word co-occurrence etc.) of natural language. Such statistics are relevant to meaning because of the Distributional Principle that ‘words of similar meaning tend to occur in similar contexts’. Computational systems, such as Latent Semantic Analysis, have substantiated the viability of distributional learning of word meaning, by showing that semantic similarities between words can be accurately estimated from analysis of the distributional statistics of a natural language corpus. We consider whether appearance similarities can also be learnt in a distributional mode. As grounds for such a mode we advance the Appearance Hypothesis that ‘words with referents of similar appearance tend to occur in similar contexts’. We assess the viability of such learning by looking at the performance of a computer system that interpolates, on the basis of distributional and appearance similarity, from words that it has been explicitly taught the appearance of, in order to identify and name objects that it has not been taught about. Our experiment tests with a set of 660 simple concrete noun words. Appearance information on words is modelled using sets of images of examples of the word. Distributional similarity is computed from a standard natural language corpus. Our computation results support the viability of distributional learning of appearance.     

Beyond Word Frequency: Bursts,Lulls, and Scaling in the Temporal Distributions of Words

Background

Zipf''s discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication. More recent research has also identified scaling regularities in the dynamics underlying the successive occurrences of events, suggesting the possibility of similar findings for language as well.

Methodology/Principal Findings

By considering frequent words in USENET discussion groups and in disparate databases where the language has different levels of formality, here we show that the distributions of distances between successive occurrences of the same word display bursty deviations from a Poisson process and are well characterized by a stretched exponential (Weibull) scaling. The extent of this deviation depends strongly on semantic type – a measure of the logicality of each word – and less strongly on frequency. We develop a generative model of this behavior that fully determines the dynamics of word usage.

Conclusions/Significance

Recurrence patterns of words are well described by a stretched exponential distribution of recurrence times, an empirical scaling that cannot be anticipated from Zipf''s law. Because the use of words provides a uniquely precise and powerful lens on human thought and activity, our findings also have implications for other overt manifestations of collective human dynamics.     

Subset clustering of binary sequences, with an application to genomic abnormality data

This article develops a model-based approach to clustering multivariate binary data, in which the attributes that distinguish a cluster from the rest of the population may depend on the cluster being considered. The clustering approach is based on a multivariate Dirichlet process mixture model, which allows for the estimation of the number of clusters, the cluster memberships, and the cluster-specific parameters in a unified way. Such a clustering approach has applications in the analysis of genomic abnormality data, in which the development of different types of tumors may depend on the presence of certain abnormalities at subsets of locations along the genome. Additionally, such a mixture model provides a nonparametric estimation scheme for dependent sequences of binary data.     

The word landscape of the non-coding segments of the Arabidopsis thaliana genome

Background

Genome sequences can be conceptualized as arrangements of motifs or words. The frequencies and positional distributions of these words within particular non-coding genomic segments provide important insights into how the words function in processes such as mRNA stability and regulation of gene expression.

Results

Using an enumerative word discovery approach, we investigated the frequencies and positional distributions of all 65,536 different 8-letter words in the genome of Arabidopsis thaliana. Focusing on promoter regions, introns, and 3' and 5' untranslated regions (3'UTRs and 5'UTRs), we compared word frequencies in these segments to genome-wide frequencies. The statistically interesting words in each segment were clustered with similar words to generate motif logos. We investigated whether words were clustered at particular locations or were distributed randomly within each genomic segment, and we classified the words using gene expression information from public repositories. Finally, we investigated whether particular sets of words appeared together more frequently than others.

Conclusion

Our studies provide a detailed view of the word composition of several segments of the non-coding portion of the Arabidopsis genome. Each segment contains a unique word-based signature. The respective signatures consist of the sets of enriched words, 'unwords', and word pairs within a segment, as well as the preferential locations and functional classifications for the signature words. Additionally, the positional distributions of enriched words within the segments highlight possible functional elements, and the co-associations of words in promoter regions likely represent the formation of higher order regulatory modules. This work is an important step toward fully cataloguing the functional elements of the Arabidopsis genome.     

Development and regeneration of the retinotectal map in goldfish: a computational study

We present a simple computational model to study the interplay of activity-dependent and intrinsic processes thought to be involved in the formation of topographic neural projections. Our model consists of two input layers which project to one target layer. The connections between layers are described by a set of synaptic weights. These weights develop according to three interacting developmental rules: (i) an intrinsic fibre-target interaction which generates chemospecific adhesion between afferent fibres and target cells; (ii) an intrinsic fibre-fibre interaction which generates mutual selective adhesion between the afferent fibres; and (iii) an activity-dependent fibre-fibre interaction which implements Hebbian learning. Additionally, constraints are imposed to keep synaptic weights finite. The model is applied to a set of eleven experiments on the regeneration of the retinotectal projection in goldfish. We find that the model is able to reproduce the outcome of an unprecedented range of experiments with the same set of model parameters, including details of the size of receptive and projective fields. We expect this mathematical framework to be a useful tool for the analysis of developmental processes in general. <br>     

Numerical comparison of several approximations of the word count distribution in random sequences.

The exact distribution of word counts in random sequences and several approximations have been proposed in the past few years. The exact distribution has no theoretical limit but may require prohibitive computation time. On the other hand, approximate distributions can be rapidly calculated but, in practice, are only accurate under specific conditions. After making a survey of these distributions, we compare them according to both their accuracy and computational cost. Rules are suggested for choosing between Gaussian approximations, compound Poisson approximation, and exact distribution. This work is illustrated with the detection of exceptional words in the phage Lambda genome.     

Identification of tissue differentiation rates in a mechanobiological model of fracture healing

As a basis for model-based analysis of the processes in secondary fracture healing, a dynamical model is presented that characterises the physiological status in the fracture area by the location-dependent composition of tissues. Five types of tissue are distinguished: connective tissue, cartilage, bone, haematoma and avascular bone. A rule base is given that describes dynamical tissue differentiation processes. The rules consider not only a mechanical stimulus but also osteogenic and a vasculative factors as biological stimuli. Within this model structure, it is possible, e.g., to distinguish intramembranous from endochondral ossification processes. An objective function is introduced to assess accordance between the model-based simulation results and reference healing stages. By minimising this objective function, relevant tissue differentiation rates can be determined. For a reference process of secondary fracture healing it could be shown that the intramembranous ossification rate of 0.313%/day (from connective tissue to bone) is much smaller than the endochondral ossification rate of 1.136%/day (from cartilage to bone). In order to verify the model approach, it is transferred to simulate long bone distraction. Results show that healing patterns of bone distraction can be predicted. Using this method, it is possible to identify model parameters for individual subjects. This will allow a patient-specific analysis of tissue healing processes in future.     

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.     

Grounding word learning in space

Humans and objects, and thus social interactions about objects, exist within space. Words direct listeners' attention to specific regions of space. Thus, a strong correspondence exists between where one looks, one's bodily orientation, and what one sees. This leads to further correspondence with what one remembers. Here, we present data suggesting that children use associations between space and objects and space and words to link words and objects--space binds labels to their referents. We tested this claim in four experiments, showing that the spatial consistency of where objects are presented affects children's word learning. Next, we demonstrate that a process model that grounds word learning in the known neural dynamics of spatial attention, spatial memory, and associative learning can capture the suite of results reported here. This model also predicts that space is special, a prediction supported in a fifth experiment that shows children do not use color as a cue to bind words and objects. In a final experiment, we ask whether spatial consistency affects word learning in naturalistic word learning contexts. Children of parents who spontaneously keep objects in a consistent spatial location during naming interactions learn words more effectively. Together, the model and data show that space is a powerful tool that can effectively ground word learning in social contexts.     

A Model-Based Approach for Making Ecological Inference from Distance Sampling Data

Summary .  We consider a fully model-based approach for the analysis of distance sampling data. Distance sampling has been widely used to estimate abundance (or density) of animals or plants in a spatially explicit study area. There is, however, no readily available method of making statistical inference on the relationships between abundance and environmental covariates. Spatial Poisson process likelihoods can be used to simultaneously estimate detection and intensity parameters by modeling distance sampling data as a thinned spatial point process. A model-based spatial approach to distance sampling data has three main benefits: it allows complex and opportunistic transect designs to be employed, it allows estimation of abundance in small subregions, and it provides a framework to assess the effects of habitat or experimental manipulation on density. We demonstrate the model-based methodology with a small simulation study and analysis of the Dubbo weed data set. In addition, a simple ad hoc method for handling overdispersion is also proposed. The simulation study showed that the model-based approach compared favorably to conventional distance sampling methods for abundance estimation. In addition, the overdispersion correction performed adequately when the number of transects was high. Analysis of the Dubbo data set indicated a transect effect on abundance via Akaike's information criterion model selection. Further goodness-of-fit analysis, however, indicated some potential confounding of intensity with the detection function.     

Logical-Semantic Analysis and the Development of L.S. Vygotsky's Ideas About “Units” and “Elements” of Psychological Systems

Based on an analysis of L.S. Vygotsky's concepts of “units” and “elements” of psychological systems, this article highlights five of their attributes. It shows that these attributes are logically symmetrical, since in their wording they can be converted into one another by negation or by replacing some words with their opposites. This suggests that the concepts of the “unit” and “element” of a system are different poles of one theoretical construct of the activity of human psychology. Thus methods for the study of psychological systems by breaking them down into elements or by separating them into units can be seen as complementary. The article describes differences among the concepts of “unit,” “minimal unit,” and “cell” of a psychological system. It reviews several problems that are solvable using the “method of units,” as well as some concepts of the theory of psychological systems that are understood as holistic, conceptual, and active processes and/or results of human interaction with the world. Among the examples of such systems are “systems of psychological functions” (according to Vygotsky), as well as separate activities (according to A.N. Leontiev), human actions and operations (interactions with the world on the level of objects and mental or physical means). The “component” of a psychological system is defined as any “something” that in some sense belongs to or is included in human interaction with the world. A component that belongs to the system is called an “element” of it, but a component that is included in the functioning and development of the system is called a “part” of it. The article presents the mathematical and psychological foundation of these definitions. It identifies and discusses the substantial (independently existing) components of psychological systems and their attributes (properties and conditions). It describes the relationships between them using the bipolar theoretical constructs “part-element” and “substantial-attributive” component of a system.