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Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively…
The construction of physically relevant low dimensional state models, and the design of appropriate measurements are key issues in tackling quantum state tomography for large dimensional systems. We consider the statistical problem of…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
Information criteria such as Akaike's (AIC) and Bayes' (BIC) are widely used for model selection in physics and beyond, quantifying the tradeoff between model complexity and goodness-of-fit to enforce parsimony. However, their derivation…
In the information-based paradigm of inference, model selection is performed by selecting the candidate model with the best estimated predictive performance. The success of this approach depends on the accuracy of the estimate of the…
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…
Information of interest can often only be extracted from data by model fitting. When the functional form of such a model can not be deduced from first principles, one has to make a choice between different possible models. A common approach…
We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which…
Quantum state estimation (or state tomography) is an indispensable task in quantum information processing. Because full state tomography that determines all elements of the density matrix is computationally demanding, one usually takes the…
We report our theoretical and experimental investigations into errors in quantum state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating…
While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation…
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…
Effective model selection is critical in symbolic regression (SR) to identify mathematical expressions that balance accuracy and complexity, and have low expected error on unseen data. Many modern implementations of genetic programming (GP)…
Model selection is a pivotal process in the quantitative sciences, where researchers must navigate between numerous candidate models of varying complexity. Traditional information criteria, such as the corrected Akaike Information Criterion…
Akaike's information criterion (AIC) is a measure of the quality of a statistical model for a given set of data. We can determine the best statistical model for a particular data set by the minimization of the AIC. Since we need to evaluate…
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…
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.…
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 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,…
The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect…