27 research outputs found
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
Proceedings of the Conference on Production Systems and Logistics: CPSL 2022
[no abstract available
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Forecasting monthly airline passenger numbers with small datasets using feature engineering and a modified principal component analysis
In this study, a machine learning approach based on time series models, different feature engineering, feature extraction, and feature derivation is proposed to improve air passenger forecasting. Different types of datasets were created to extract new features from the core data. An experiment was undertaken with artificial neural networks to test the performance of neurons in the hidden layer, to optimise the dimensions of all layers and to obtain an optimal choice of connection weights â thus the nonlinear optimisation problem could be solved directly. A method of tuning deep learning models using H2O (which is a feature-rich, open source machine learning platform known for its R and Spark integration and its ease of use) is also proposed, where the trained network model is built from samples of selected features from the dataset in order to ensure diversity of the samples and to improve training. A successful application of deep learning requires setting numerous parameters in order to achieve greater model accuracy. The number of hidden layers and the number of neurons, are key parameters in each layer of such a network. Hyper-parameter, grid search, and random hyper-parameter approaches aid in setting these important parameters. Moreover, a new ensemble strategy is suggested that shows potential to optimise parameter settings and hence save more computational resources throughout the tuning process of the models. The main objective, besides improving the performance metric, is to obtain a distribution on some hold-out datasets that resemble the original distribution of the training data. Particular attention is focused on creating a modified version of Principal Component Analysis (PCA) using a different correlation matrix â obtained by a different correlation coefficient based on kinetic energy to derive new features. The data were collected from several airline datasets to build a deep prediction model for forecasting airline passenger numbers. Preliminary experiments show that fine-tuning provides an efficient approach for tuning the ultimate number of hidden layers and the number of neurons in each layer when compared with the grid search method. Similarly, the results show that the modified version of PCA is more effective in data dimension reduction, classes reparability, and classification accuracy than using traditional PCA.</div
A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium
When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its Ï parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available
A Statistical Approach to the Alignment of fMRI Data
Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods
Differential geometric aspects of parametric estimation theory for states on finite-dimensional C*-algebras
A geometrical formulation of estimation theory for finite-dimensional
-algebras is presented. This formulation allows to deal with the
classical and quantum case in a single, unifying mathematical framework. The
derivation of the Cramer-Rao and Helstrom bounds for parametric statistical
models with discrete and finite outcome spaces is presented.Comment: 33 pages. Minor improvements. References added. Comments are welcome
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Statistical inference and computation in elliptic PDE models
Partial differential equations (PDE) are ubiquitous in describing real-world phenomena. In many statistical models, PDE are used to encode complex relationships between unknown quantities and the observed data. We investigate statistical and computational questions arising in such models, adopting an infinite-dimensional `nonparametric' framework and assuming the observed data are subject to random noise. The main PDE examples are of elliptic or parabolic type.
Chapter 2 investigates the problem of sampling from high-dimensional Bayesian posterior distributions. The main results consist of non-asymptotic computational guarantees for Langevin-type Markov chain Monte Carlo (MCMC) algorithms which scale polynomially in key quantities such as the dimension of the model, the desired precision level, and the number of available statistical measurements. The bounds hold with high probability under the distribution of the data, assuming that certain `local geometric' assumptions are fulfilled and that a good initialiser of the algorithm is available. We study a representative non-linear PDE example where the unknown is a coefficient function in a steady-state Schr\"odinger equation, and the solution to a corresponding boundary value problem is observed.
Chapter 3 studies statistical convergence rates for nonparametric Tikhonov-type estimators, which can be interpreted also as Bayesian maximum a posteriori (MAP) estimators arising from certain Gaussian process priors. The theory is derived in a general setting for non-linear inverse problems and then applied to two examples, the steady-state Schr\"odinger equation studied in Chapter \ref{sampling} and a model for the steady-state heat equation. It is shown that the rates obtained are minimax-optimal in prediction loss.
The final Chapter 4 considers a model for scalar diffusion processes with an unknown drift function which is modelled nonparametrically. It is shown that in the low frequency sampling case, when the sample consists of for some fixed sampling distance , under mild regularity assumptions, the model satisfies the local asymptotic normality (LAN) property. The key tools used are regularity estimates and spectral properties for certain parabolic and elliptic PDE related to