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Model selection is of fundamental importance to high dimensional modeling featured in many contemporary applications. Classical principles of model selection include the Kullback-Leibler divergence principle and the Bayesian principle,…

Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix.…

Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix…

Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary…

Finite mixture models are ubiquitous in modern statistical modeling, and a recurring practical issue is choosing the model order. In \citet[Sankhy\=a Series A, \textbf62, pp. 49--66]{keribin2000consistent}, the Bayesian information…

Selecting the number of regimes in Hidden Markov models is an important problem. There are many criteria that are used to select this number, such as Akaike information criterion (AIC), Bayesian information criterion (BIC), integrated…

Convolutional neural networks (CNNs) have emerged as a powerful tool for automatic modulation classification (AMC) by directly extracting discriminative features from raw in-phase and quadrature (I/Q) signals. However, deploying CNN-based…

Claeskens and Hjort (2003) constructed the focused information criterion (FIC) and developed frequentist model averaging methods using maximum likelihood estimators assuming the observations to be independent and identically distributed.…

Transient recurring phenomena are ubiquitous in many scientific fields like neuroscience and meteorology. Time inhomogenous Vector Autoregressive Models (VAR) may be used to characterize peri-event system dynamics associated with such…

Accurate model selection is a fundamental requirement for statistical analysis. In many real-world applications of graphical modelling, correct model structure identification is the ultimate objective. Standard model validation procedures…

The Akaike information criterion (AIC) is a model selection criterion widely used in practical applications. The AIC is an estimator of the log-likelihood expected value, and measures the discrepancy between the true model and the estimated…

This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…

Aim: The Akaike information Criterion (AIC) is widely used science to make predictions about complex phenomena based on an entire set of models weighted by Akaike weights. This approach (AIC model averaging; hereafter AvgAICc) is often…

Information theoretic criteria (ITC) have been widely adopted in engineering and statistics for selecting, among an ordered set of candidate models, the one that better fits the observed sample data. The selected model minimizes a penalized…

In model selection literature, two classes of criteria perform well asymptotically in different situations: Bayesian information criterion (BIC) (as a representative) is consistent in selection when the true model is finite dimensional…

In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…

Error Correcting Output Codes (ECOC) is a successful technique in multi-class classification, which is a core problem in Pattern Recognition and Machine Learning. A major advantage of ECOC over other methods is that the multi- class problem…

Model selection is a ubiquitous problem that arises in the application of many statistical and machine learning methods. In the likelihood and related settings, it is typical to use the method of information criteria (IC) to choose the most…

The uncertainty-penalized information criterion (UBIC) has been proposed as a new model-selection criterion for data-driven partial differential equation (PDE) discovery. In this paper, we show that using the UBIC is equivalent to employing…

Model selection is the problem of distinguishing competing models, perhaps featuring different numbers of parameters. The statistics literature contains two distinct sets of tools, those based on information theory such as the Akaike…