Model Selection Procedure Research Articles

Neural surprise in somatosensory Bayesian learning.

Tracking statistical regularities of the environment is important for shaping human behavior and perception. Evidence suggests that the brain learns environmental dependencies using Bayesian principles. However, much remains unknown about the employed algorithms, for somesthesis in particular. Here, we describe the cortical dynamics of the somatosensory learning system to investigate both the form of the generative model as well as its neural surprise signatures. Specifically, we recorded EEG data from 40 participants subjected to a somatosensory roving-stimulus paradigm and performed single-trial modeling across peri-stimulus time in both sensor and source space. Our Bayesian model selection procedure indicates that evoked potentials are best described by a non-hierarchical learning model that tracks transitions between observations using leaky integration. From around 70ms post-stimulus onset, secondary somatosensory cortices are found to represent confidence-corrected surprise as a measure of model inadequacy. Indications of Bayesian surprise encoding, reflecting model updating, are found in primary somatosensory cortex from around 140ms. This dissociation is compatible with the idea that early surprise signals may control subsequent model update rates. In sum, our findings support the hypothesis that early somatosensory processing reflects Bayesian perceptual learning and contribute to an understanding of its underlying mechanisms.

Modeling Multivariate Time Series With Copula-Linked Univariate D-Vines

This article proposes a novel multivariate time series model named copula-linked univariate D-vines (CuDvine), which enables the simultaneous copula-based modeling of both temporal and cross-sectional dependence for multivariate time series. To construct CuDvine, we first build a semiparametric univariate D-vine time series model (uDvine) based on a D-vine. The uDvine generalizes the existing first-order copula-based Markov chain models to Markov chains of an arbitrary-order. Building upon uDvine, we construct CuDvine by linking multiple uDvines via a parametric copula. As a simple and tractable model, CuDvine provides flexible models for marginal behavior and temporal dependence of time series, and can also incorporate sophisticated cross-sectional dependence such as time-varying and spatio-temporal dependence for high-dimensional applications. Robust and computationally efficient procedures, including a sequential model selection method and a two-stage MLE, are proposed for model estimation and inference, and their statistical properties are investigated. Numerical experiments are conducted to demonstrate the flexibility of CuDvine, and to examine the performance of the sequential model selection procedure and the two-stage MLE. Real data applications on the Australian electricity price data demonstrate the superior performance of CuDvine to traditional multivariate time series models.

Graphkit-learn: A Python library for graph kernels based on linear patterns

• Graph kernels bridge the gap between machine learning and data encoded as graphs. • Graph kernels based on linear patterns provide good performance. • A Python library for efficient computation of graph kernels is proposed. • Three strategies are provided to reduce computational complexity. • Experiments on synthesized and real-world datasets show the relevance of the library. This paper presents graphkit-learn , the first Python library for efficient computation of graph kernels based on linear patterns, able to address various types of graphs. Graph kernels based on linear patterns are thoroughly implemented, each with specific computing methods, as well as two well-known graph kernels based on non-linear patterns for comparative analysis. Since computational complexity is an Achilles’ heel of graph kernels, we provide several strategies to address this critical issue, including parallelization, the trie data structure, and the FCSP method that we extend to other kernels and edge comparison. All proposed strategies save orders of magnitudes of computing time and memory usage. Moreover, all the graph kernels can be simply computed with a single Python statement, thus are appealing to researchers and practitioners. For the convenience of use, an advanced model selection procedure is provided for both regression and classification problems. Experiments on synthesized datasets and 11 real-world benchmark datasets show the relevance of the proposed library.

Nutritional status and anxious and depressive symptoms in anorexia nervosa: a prospective study

The interweaving of malnutrition and symptoms of anxiety and depression in anorexia Nervosa (AN) is mentioned without any consensus regarding the course of anxious-depressive symptoms in relation to nutritional status in the course of treatment of patients with AN. The objectives of the current study in a large sample of AN inpatients were to assess the relationships between anxiety and depression symptoms and nutritional status both over the course of inpatient treatment and at discharge. 222 consecutive inpatients with AN (DSM-IV TR) were assessed (entrance and discharge) for duration of illness, psychiatric treatments, sociodemographic data and with psychometric scales for different psychopathological symptoms [depressive (BDI), anxiety and depressive (HAD scale), obsessive–compulsive (MOCI) and social phobia (LSAS fear score)]. Nutritional status was assessed with Body Mass Index (BMI) and body composition by bioelectrical impedance. The Fat free mass index [FFMI = FFM (kg)/height (m2)] was considered for the analysis. Two models were developed where the dependent variables were each psychopathological score at discharge (BDI, HAD anxiety, MOCI, and LSAS fear) in the cross-sectional model, and their variation in the longitudinal model (where a positive score reflected symptom decrease at discharge). A fixed set of predictors, defined on presumed clinical and statistical relevance (FFMI in the cross-sectional model and Variation of FFMI in the longitudinal model), were considered in each model, without any model selection procedure. This is the first study to confirm a positive relationship between the course of eating disorder symptoms and that of anxious-depressive symptoms during inpatient treatment of AN even after adjustment on a vast array of possibly confounding factors.

Bayesian Multiple Change-Points Detection in a Normal Model with Heterogeneous Variances

This study considers the problem of multiple change-points detection. For this problem, we develop an objective Bayesian multiple change-points detection procedure in a normal model with heterogeneous variances. Our Bayesian procedure is based on a combination of binary segmentation and the idea of the screening and ranking algorithm (Niu and Zhang in Ann Appl Stat 6:1306–1326, 2012). Using the screening and ranking algorithm, we can overcome the drawbacks of binary segmentation, as it cannot detect a small segment of structural change in the middle of a large segment or segments of structural changes with small jump magnitude. We propose a detection procedure based on a Bayesian model selection procedure to address this problem in which no subjective input is considered. We construct intrinsic priors for which the Bayes factors and model selection probabilities are well defined. We find that for large sample sizes, our method based on Bayes factors with intrinsic priors is consistent. Moreover, we compare the behavior of the proposed multiple change-points detection procedure with existing methods through a simulation study and two real data examples.

Model selection for time series with nonlinear trend

A two-step model selection procedure is proposed for autoregressive and moving-average (ARMA) model class. It is an adaptive least absolute shrinkage and selection operator (adLASSO) type model selection method that simultaneously chooses both the orders and significant lagged variables when the autoregressive and moving-average (ARMA) time series is contaminated with a nonlinear trend. The adLASSO is applied not to the observations, but to the detrended residuals. The proposed two-step adLASSO model selection procedure under some conditions can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The simulation studies show that the proposed method performs well with sample size as small as 50. The application of the method is illustrated by the annual varve thickness data collected from a location in Massachusetts.

Latitude does not influence cavity entrance orientation of South American avian excavators

AbstractIn the Northern Hemisphere, several avian cavity excavators (e.g., woodpeckers) orient their cavities increasingly toward the equator as latitude increases (i.e. farther north), and it is proposed that they do so to take advantage of incident solar radiation at their nests. If latitude is a key driver of cavity orientations globally, this pattern should extend to the Southern Hemisphere. Here, we test the prediction that cavities are oriented increasingly northward at higher (i.e. colder) latitudes in the Southern Hemisphere and describe the preferred entrance direction(s) of 1,501 cavities excavated by 25 avian species (n = 22 Picidae, 2 Trogonidae, 1 Furnariidae) across 12 terrestrial ecoregions (15°S to 55°S) in South America. We used Bayesian projected normal mixed-effects models for circular data to examine the influence of latitude, and potential confounding factors, on cavity orientation. Also, a probability model-selection procedure was used to simultaneously examine multiple orientation hypotheses in each ecoregion to explore underlying cavity-orientation patterns. Contrary to predictions, and patterns from the Northern Hemisphere, birds did not orient their cavities more toward the equator with increasing latitude, suggesting that latitude may not be an important underlying selective force shaping excavation behavior in South America. Moreover, unimodal cavity-entrance orientations were not frequent among the ecoregions analyzed (only in 4 ecoregions), whereas bimodal (in 5 ecoregions) or uniform (in 3 ecoregions) orientations were also present, although many of these patterns were not very clear. Our results highlight the need to include data from under-studied biotas and regions to improve inferences at macroecological scales. Furthermore, we suggest a re-analysis of Northern Hemisphere cavity orientation patterns using a multi-model approach, and a more comprehensive assessment of the role of environmental factors as drivers of cavity orientation at different spatial scales in both hemispheres.

A partial least squares approach for function-on-function interaction regression

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The direct estimation of a function-on-function regression model is usually an ill-posed problem. To overcome this difficulty, in practice, the functional data that belong to the infinite-dimensional space are generally projected into a finite-dimensional space of basis functions. The function-on-function regression model is converted to a multivariate regression model of the basis expansion coefficients. In the estimation phase of the proposed method, the functional variables are approximated by a finite-dimensional basis function expansion method. We show that the partial least squares regression constructed via a functional response, multiple functional predictors, and quadratic/interaction terms of the functional predictors is equivalent to the partial least squares regression constructed using basis expansions of functional variables. From the partial least squares regression of the basis expansions of functional variables, we provide an explicit formula for the partial least squares estimate of the coefficient function of the function-on-function regression model. Because the true forms of the models are generally unspecified, we propose a forward procedure for model selection. The finite sample performance of the proposed method is examined using several Monte Carlo experiments and two empirical data analyses, and the results were found to compare favorably with an existing method.

A MOM-based ensemble method for robustness, subsampling and hyperparameter tuning

Hyperparameter tuning and model selection are important steps in machine learning. Unfortunately, classical hyperparameter calibration and model selection procedures are sensitive to outliers and heavy-tailed data. In this work, we construct a selection procedure which can be seen as a robust alternative to cross-validation and is based on a median-of-means principle. Using this procedure, we also build an ensemble method which, trained with algorithms and corrupted heavy-tailed data, selects an algorithm, trains it with a large uncorrupted subsample and automatically tunes its hyperparameters. In particular, the approach can transform any procedure into a robust to outliers and to heavy-tailed data procedure while tuning automatically its hyperparameters. The construction relies on a divide-and-conquer methodology, making this method easily scalable even on a corrupted dataset. This method is tested with the LASSO which is known to be highly sensitive to outliers.

Explainable fintech lending

Lending to Small and Medium Enterprises (SME) is facilitated by the availability of advanced Machine Learning (ML) methods, embedded in financial technologies, which can accurately predict financial performance from the many data sources available. However, despite their high predictive accuracy, ML models may not provide sufficient explanations to investors and, therefore, may not be adequate for informed decision-making. We propose a financial machine learning model that is both accurate and explainable. To reach this aim, we propose to enhance random forest models with a model selection procedure that progressively removes the least explainable variable, according to the Shapley value method. We apply our proposal to 2,049 SMEs for which yearly financial performance indicators are available. Our results show that both the default and the expected return of SMEs can be well predicted and explained by a small set of indicators deduced from their balance sheets.

A post COVID Machine Learning approach in Teaching and Learning methodology to alleviate drawbacks of the e-whiteboards

Deep learning has paved the way for critical and revolutionary applications in almost every field of life in general. Ranging from engineering to healthcare, machine learning and deep learning has left its mark as the state-of-the-art technology application which holds the epitome of a reasonable high benchmarked solution. Incorporating neural network architectures into applications has become a common part of any software development process. In this paper, we perform a comparative analysis on the different transfer learning approaches in the domain of hand-written digit recognition. We use two performance measures, loss and accuracy. We later visualize the different results for the training and validation datasets and reach to a unison conclusion. This paper aims to target the drawbacks of the electronic whiteboard with simultaneous focus on the suitable model selection procedure for the digit recognition problem. © 2021 Tamkang University. All Rights Reserved.

Gaussian linear model selection in a dependent context

In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the penalty function, ensuring that the penalized estimator among a collection of models satisfies an oracle inequality. Then we derive a penalty shape involving the spectral radius of the covariance matrix of the errors, which can be chosen proportional to the dimension when the error process is stationary and short range dependent. However, this penalty can be too rough in some cases, in particular when the error process is long range dependent. In a second part, we focus on the fixed-design regression model assuming that the error process is a stationary Gaussian process. We propose a model selection procedure in order to estimate the mean function via piecewise polynomials on a regular partition, when the error process is either short range dependent, long range dependent or anti-persistent. We present different kinds of penalties, depending on the memory of the process. For each case, an adaptive estimator is built, and the rates of convergence are computed. Thanks to several sets of simulations, we study the performance of these different penalties for all types of errors (short memory, long memory and anti-persistent errors). Finally, we give an application of our method to the well-known Nile data, which clearly shows that the type of dependence of the error process must be taken into account.

Elastic modulus formulation of cementitious materials incorporating carbon nanotubes: Probabilistic approach

Carbon nanotube (CNT) is one of the most promising nanomaterials to increase the elastic modulus of cementitious composites. However, CNT characteristics, dispersion procedure, and matrix composition/hydration are critical and correlated with a high degree of uncertainty in achieving a desirable performance. This paper proposes a mechanics-based model to predict the elastic modulus of CNT reinforced cementitious materials based on the Halpin-Tsai equation. The current study employs a probabilistic approach to consider the influences of multiple experimental variables and various sources of uncertainty associated with them. To this end, first, a Bayesian methodology is adopted to perform the model validation, evaluation, and selection procedures using extensive literature test data. Then, the optimum ranges of variables are found to maximize the chance of achieving a certain target modulus (herein, 50% more than control) using a reliability analysis. The proposed model suggests that the highest elastic modulus is achieved when using CNT aspect ratio ranges from 400 to 800 and concentration between 0.08 and 0.18c-wt%. Also, the experimentally observed elastic modulus and the proposed probabilistic model exhibit a similar trend. For example, the importance of hydration age increases as CNT concentration increases.Finally, the proposed model can be used to reliably predict the elastic modulus, guiding future researchers to design more efficiently.

Production of mobile invertebrate communities on shallow reefs from temperate to tropical seas.

Primary productivity of marine ecosystems is largely driven by broad gradients in environmental and ecological properties. By contrast, secondary productivity tends to be more variable, influenced by bottom-up (resource-driven) and top-down (predatory) processes, other environmental drivers, and mediation by the physical structure of habitats. Here, we use a continental-scale dataset on small mobile invertebrates (epifauna), common on surfaces in all marine ecosystems, to test influences of potential drivers of temperature-standardized secondary production across a large biogeographic range. We found epifaunal production to be remarkably consistent along a temperate to tropical Australian latitudinal gradient of 28.6°, spanning kelp forests to coral reefs (approx. 3500 km). Using a model selection procedure, epifaunal production was primarily related to biogenic habitat group, which explained up to 45% of total variability. Production was otherwise invariant to predictors capturing primary productivity, the local biomass of fishes (proxy for predation pressure), and environmental, geographical, and human impacts. Highly predictable levels of epifaunal productivity associated with distinct habitat groups across continental scales should allow accurate modelling of the contributions of these ubiquitous invertebrates to coastal food webs, thus improving understanding of likely changes to food web structure with ocean warming and other anthropogenic impacts on marine ecosystems.

News and Idiosyncratic Volatility: The Public Information Processing Hypothesis*

Abstract Motivated by the recent availability of extensive electronic news databases and advent of new empirical methods, there has been renewed interest in investigating the impact of financial news on market outcomes for individual stocks. We develop the information processing hypothesis of return volatility to investigate the relation between firm-specific news and volatility. We propose a novel dynamic econometric specification and test it using time series regressions employing a machine learning model selection procedure. Our empirical results are based on a comprehensive dataset comprised of more than 3 million news items for a sample of 28 large U.S. companies. Our proposed econometric specification for firm-specific return volatility is a simple mixture model with two components: public information and private processing of public information. The public information processing component is defined by the contemporaneous relation with public information and volatility, while the private processing of public information component is specified as a general autoregressive process corresponding to the sequential price discovery mechanism of investors as additional information, previously not publicly available, is generated and incorporated into prices. Our results show that changes in return volatility are related to public information arrival and that including indicators of public information arrival explains on average 26% (9–65%) of changes in firm-specific return volatility.

Bayesian Modeling for Epistasis Analysis Using Data-Driven Reversible Jump.

We propose a procedure for modeling a phenotype using QTLs which estimate the additive and dominance effects of genotypes and epistasis. The estimation of the model is implemented through a Bayesian approach which uses the data-driven reversible jump (DDRJ) for multiple QTL mapping and model selection. We compare the DDRJ's performance with the usual reversible jump (RJ), QTLBim, multiple interval mapping (MIM) and LASSO using real and simulated data sets. The DDRJ outperforms the available methods to estimate the number of QTLs in epistatic models and it identifies their locations in the genome, without increasing the number of false-positive QTLs in the considered data. Since QTL mapping is a regression model involving complex non-observable variables and their interactions, the model selection procedure proposed here is also useful in other areas of research. The application for identifying main and epistatic relevant QTLs to systolic blood pressure after salt intervention is our main motivation.

Improved signal processing observed with semi-Markov noises

This paper considers the problem of improved adaptive estimating a periodic signal observed in the transmission channel with the dependent noise defined by semi-Markov processes with unknown probabilities and spectral characteristics. Improved adaptive model selection procedure is proposed. The comparison between improved and least squares methods is studied. Sharp oracle inequality for the procedure risk is obtained. The efficiency of the proposed procedure is established. The Monte Carlo simulation results are given.

Statistical inference of assortative community structures

We develop a principled methodology to infer assortative communities in networks based on a nonparametric Bayesian formulation of the planted partition model. We show that this approach succeeds in finding statistically significant assortative modules in networks, unlike alternatives such as modularity maximization, which systematically overfits both in artificial as well as in empirical examples. In addition, we show that our method is not subject to a resolution limit, and can uncover an arbitrarily large number of communities, as long as there is statistical evidence for them. Our formulation is amenable to model selection procedures, which allow us to compare it to more general approaches based on the stochastic block model, and in this way reveal whether assortativity is in fact the dominating large-scale mixing pattern. We perform this comparison with several empirical networks, and identify numerous cases where the network's assortativity is exaggerated by traditional community detection methods, and we show how a more faithful degree of assortativity can be identified.

Levels of biological plausibility.

Notions of mechanism, emergence, reduction and explanation are all tied to levels of analysis. I cover the relationship between lower and higher levels, suggest a level of mechanism approach for neuroscience in which the components of a mechanism can themselves be further decomposed and argue that scientists' goals are best realized by focusing on pragmatic concerns rather than on metaphysical claims about what is ‘real'. Inexplicably, neuroscientists are enchanted by both reduction and emergence. A fascination with reduction is misplaced given that theory is neither sufficiently developed nor formal to allow it, whereas metaphysical claims of emergence bring physicalism into question. Moreover, neuroscience's existence as a discipline is owed to higher-level concepts that prove useful in practice. Claims of biological plausibility are shown to be incoherent from a level of mechanism view and more generally are vacuous. Instead, the relevant findings to address should be specified so that model selection procedures can adjudicate between competing accounts. Model selection can help reduce theoretical confusions and direct empirical investigations. Although measures themselves, such as behaviour, blood-oxygen-level-dependent (BOLD) and single-unit recordings, are not levels of analysis, like levels, no measure is fundamental and understanding how measures relate can hasten scientific progress.This article is part of the theme issue ‘Key relationships between non-invasive functional neuroimaging and the underlying neuronal activity'.

Jointly Determining the State Dimension and Lag Order for Markov-Switching Vector Autoregressive Models

This paper studies the problem of joint identification of the state dimension and lag order for a class of Markov-switching vector autoregressive (MS-VAR) models, in which all parameters are presumed to be regime-dependent. To this end, three complexity-penalized criteria AIC^{MS}, HQC^{MS} and SIC^{MS} are considered, and a new criterion AIC_c^{MS} is derived by minimizing the Kullback-Leibler (KL) divergence. The efficacy of the procedure is evaluated by means of Monte Carlo experiments. We illustrate the usefulness of the joint model selection procedure with empirical applications to the modeling of business cycles in the U.S. and Australia.