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1

General and regional cross station assessment of machine learning models for estimating reference evapotranspiration

Zouzou Yasser, Citakoglu Hatice

Acta Geophysica

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2023

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Vol. 71, no. 2

927--947

EN

Significant research has been done on estimating reference evapotranspiration (ET0) from limited climatic measurements using machine learning (ML) to facilitate the acquirement of ET0 values in areas with limited access to weather stations. However, the spatial generalizability of ET0 estimating ML models is still questionable, especially in regions with significant climatic variation like Turkey. Aiming at exploring this generalizability, this study compares two ET0 modeling approaches: (1) one general model covering all of Turkey, (2) seven regional models, one model for each of Turkey’s seven regions. In both approaches, ET0 was predicted using 16 input combinations and 3 ML methods: support vector regression (SVR), Gaussian process regression (GPR), and random forest (RF). A cross-station evaluation was used to evaluate the models. Results showed that the use of regional models created using SVR and GPR methods resulted in a reduction in root mean squared error (RMSE) in comparison with the general model approach. Models created using the RF method suffered from overfitting in the regional models’ approach. Furthermore, a randomization test showed that the reduction in RMSE when using these regional models was statistically significant. These results emphasize the importance of defining the spatial extent of ET0 estimating models to maintain their generalizability.

2

Supervisory optimal control using machine learning for building thermal comfort

Abdufattokhov Shokhjakhon, Mahamatov Nurilla, Ibragimova Kamila, Gulyamova Dilfuza, Yuldashev Dilyorjon

Operations Research and Decisions

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2022

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Vol. 32, No. 4

1--15

EN

For the past few decades, control and building engineering communities have been focusing on thermal comfort as a key factor in designing sustainable building evaluation methods and tools. However, estimating the indoor air temperature of buildings is a complicated task due to the nonlinear and complex building dynamics characterised by the time-varying environment with disturbances. The primary focus of this paper is designing a predictive and probabilistic room temperature model of buildings using Gaussian processes (GPs) and incorporating it into model predictive control (MPC) to minimise energy consumption and provide thermal comfort satisfaction. The full probabilistic capabilities of GPs are exploited from two perspectives: the mean prediction is used for the room temperature model, while the uncertainty is involved in the MPC objective not to lose the desired performance and design a robust controller. We illustrated the potential of the proposed method in a numerical example with simulation results.

3

Extremes of order statistics of stationary Gaussian processes

Zhao C.

Probability and Mathematical Statistics

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2018

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Vol. 38, Fasc. 1

61--75

EN

Let {Xi(t), t ≥ 0}, 1 ≤ i ≤ n, be mutually independent and identically distributed centered stationary Gaussian processes. Under some mild assumptions on the covariance function, we derive an asymptotic expansion of P [formula] ]X(r) (t) ≤ u) as u → ∞, where mr(u) = (P([formula] X(r) (t) > u))−1 (1 + o(1)), and {X(r) (t), t ≥ 0} is the rth order statistic process of {Xi(t), t ≥ 0}, 1 ≤ i, r ≤ n. As an application of the derived result, we analyze the asymptotics of supremum of the order statistic process of stationary Gaussian processes over random intervals.

4

Supervised Machine Learning with Control Variates for American Option Pricing

Mu G., Godina T., Maffia A., Sun Y. C.

Foundations of Computing and Decision Sciences

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2018

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Vol. 43, No. 3

207--217

EN

In this paper, we make use of a Bayesian (supervised learning) approach in pricing American options via Monte Carlo simulations. We first present Gaussian process regression (Kriging) approach for American options pricing and compare its performance in estimating the continuation value with the Longstaff and Schwartz algorithm. Secondly, we explore the control variates technique in combination with Kriging to further improve the estimation of the continuation value. This method allows to reduce dramatically the standard errors and to improve the stability of the Kriging approach. For illustrative purposes, we use American put options on a stock whose dynamics is given by Heston model, and use European options on the same stock as control variates.

5

New interpolations between classical and free Gaussian processes

Buchholz A.

Probability and Mathematical Statistics

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2015

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Vol. 35, Fasc. 2

181--189

EN

In this paper we present the base of a general technique to derive new positive definite functions on pairings from already known ones. To describe this technique we use two concrete applications. The first one refers to the function depending on the number of connected components, the second one to the function depending on the number of crossings. In the first application we get a new family of functions identifying nontrivial connected components.

6

The Use of Genetic Algorithms for Searching Parameter Space in Gaussian Process Modeling

Krok A.

Journal of Telecommunications and Information Technology

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2015

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nr 3

58--63

EN

The aim of the paper is to present the possibilities of modeling the experimental data by Gaussian processes. Genetic algorithms are used for finding the Gaussian process parameters. Comparison of data modeling accuracy is made according to neural networks learned by Kalman filtering. Concrete hysteresis loops obtained by the experiment of cyclic loading are considered as the real data time series.

7

Metric entropy and the small deviation problem for stable processes

Aurzada F.

Probability and Mathematical Statistics

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2007

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Vol. 27, Fasc. 2

261--274

EN

The famous connection between metric entropy and small deviation probabilities of Gaussian processes was discovered by Kuelbs and Li in [6] and completed by Li and Linde in [9]. The question whether similar connections exist for other types of processes has remained open ever since. In [10], Li and Linde propose a first approach to this problem for stable processes. The present article clarifies the question completely for symmetric stable processes.

8

Curse of dimensionality in approximation of random fields

Lifshits M. A., Tulyakova V.

Probability and Mathematical Statistics

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2006

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Vol. 26, Fasc. 1

97--112

EN

Consider a random field of tensor product-type X(t), t∈[0,1]d, given by [formula] where (λ(i))i>0∈l2(φi)i>0 is an orthonormal system in L2 [0, 1] and (ξk)k∈Nd are non-correlated random variables with zero mean and unit variance. We investigate the quality of approximation (both in the average and in the probabilistic sense) to X by the n-term partial sums Xn minimizing the quadratic error E‖X‒Xn‖2, In the first part of the paper we consider the case of fixed dimension d. In the second part, following the suggestion of H. Woźniakowski, we consider the same problem for d→∞. We show that, for any fixed level of relative error, approximation complexity increases exponentially and we find the ex- plosion coefficient. We also show that the behavior of the probabilistic and average complexity is essentially the same in the large domain of parameters.

9

Martingale characterizations of stochastic processes on compact groups

Voit M.

Probability and Mathematical Statistics

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1999

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Vol. 19, Fasc. 2

389--405

EN

By a classical result of P. Lévy, the Brownian motion (Bt)t≥0 on R may be characterized as a continuous process on R such that (Bt)t≥0 and (B2t - t)t≥0 are martingales. Generalizations of this result are usually obtained in the setting of the so-called martingale problem. This paper contains a variant of the martingale problem for stochastic processes on locally compact groups with independent stationary increments that is based on irreducible unitary representations. In particular, for Gaussian processes on compact Lie groups, analogues of the Lévy-characterization above are obtained. It turns out that for certain compact Lie groups even the continuity assumption in this characterization can be dropped.