Semiparametric Bayesian networks for continuous data

Boukabour, Seloua; Masmoudi, Afif

doi:10.1080/03610926.2020.1738486

Cited by 8 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another direction is to consider same estimators grounded on bias reduction technique (see [9], [31]), which requires non trivial mathematics and goes therefore beyond the scope of the present paper. Finally, we can also explore the idea developed in the recent work of [4] through considering some semi-parametric Bayesian networks approaches based on the current work.…”

Section: Discussionmentioning

confidence: 99%

Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

Slama

Slaoui

et al. 2022

Stat., optim. inf. comput.

View full text Add to dashboard Cite

In this research paper, we set forward a non-parametric multivariate recursive kernel regression estimator under missing data using the propensity score approach in order to describe writing word production. Our main objective is to explore cognitive processes and mental representations mobilized when a human being prepares to write a word according to the idea developed in Perret and Olive (2019). We investigate the asymptotic properties of the proposed recursive estimator and compare them to the well known Nadaraya-Watson’s regression estimator. We calculate the bias and the variance of the proposed estimator which depend on the choice of some parameters such as the stepsize and the bandwidth. We examine some data-driven procedures to select these parameters. Thus, we demonstrate that, under some optimal choices of these parameters, the MSE (Mean Squared Error) of the proposed estimator can be smaller than the one obtained by using Nadaraya Watson’s regression estimator. The elaborated estimator is then applied to the behavioral data to classify some participants in groups. This classification may stand for a departure point to tackle written behavior variations.

show abstract

Section: Discussionmentioning

confidence: 99%

Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

Slama

Slaoui

et al. 2022

Stat., optim. inf. comput.

View full text Add to dashboard Cite

show abstract

“…Moreover, we plan to make extensions of our method in the future and to consider the functional data (see, Slaoui [37,38]) to built a semi-recursive Bernstein estimator for regression function. We plan also to extend our estimators by considering the recursive nonparametric estimation for Bayesian networks (see for instance the recent paper in this subject Boukabour and Masmoudi [4]).…”

Section: Discussionmentioning

confidence: 99%

“…We consider three sample sizes n = 50, n = 100 and n = 500, three regression functions (a) r(x) = cos(x), (b) r(x) = 0.3 exp −x 2 /2 + 0.7 exp −(x − 1) 2 /2 , (c) r(x) = 1 + 0.6x, and three densities of X, the beta density B(3, 5), the beta mixture density 0.5B(2, 1) + 0.5B (1,4) and the truncated standard normal density N [0,1] (0, 1). We consider six estimators: our non-recursive Bernstein estimator r n defined in (1), Nadaraya-Watson's estimator r N W n proposed in (11), two proposed recursive Bernstein estimators r n,1 and r n,2 introduced in (5) with stepsize (γ n ) = (n −1 ) and (γ n ) = (n −0.9 ) respectively and finally two Generalized Révész's estimators r GR n,1 and r GR n,2 defined in ( 12) using the same stepsizes as the one previously used in r n .…”

Section: Simulations We Consider the Regression Modelmentioning

confidence: 99%

Recursive and non-recursive regression estimators using Bernstein polynomials

Slaoui

Jmaei²

2022

Theory of Stochastic Processes

View full text Add to dashboard Cite

If a regression function has a bounded support, the kernel estimates often exceed the boundaries and are therefore biased on and near these limits. In this paper, we focus on mitigating this boundary problem. We apply Bernstein polynomials and the Robbins-Monro algorithm to construct a non-recursive and recursive regression estimator. We study the asymptotic properties of these estimators, and we compare them with those of the Nadaraya-Watson estimator and the generalized Révész estimator introduced by [21]. In addition, through some simulation studies, we show that our non-recursive estimator has the lowest integrated root mean square error (ISE) in most of the considered cases. Finally, using a set of real data, we demonstrate how our non-recursive and recursive regression estimators can lead to very satisfactory estimates, especially near the boundaries.

show abstract

“…Nonparametric or semiparametric BN development has received considerable attention in recent years (Marcot and Penman, 2019), with a number of promising developments (e.g. Masmoudi and Masmoudi, 2019;Boukabour and Masmoudi, 2020;Hanea et al, 2015), and we expect that nonparametric continuous BN algorithms will increasingly become available in commonly used BN software. However, the simplicity of the normal approximation used in GBNs means they are likely to remain a good first choice.…”

Section: Continuous Gbns For Environmental Predictionmentioning

confidence: 99%

Seasonal forecasting of lake water quality and algal bloom risk using a continuous Gaussian Bayesian network

Jackson-Blake

Clayer

Haande

et al. 2022

Hydrol. Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. Freshwater management is challenging, and advance warning that poor water quality was likely, a season ahead, could allow for preventative measures to be put in place. To this end, we developed a Bayesian network (BN) for seasonal lake water quality prediction. BNs have become popular in recent years, but the vast majority are discrete. Here, we developed a Gaussian Bayesian network (GBN), a simple class of continuous BN. The aim was to forecast, in spring, mean total phosphorus (TP) and chlorophyll a (chl a) concentration, mean water colour, and maximum cyanobacteria biovolume for the upcoming growing season (May–October) in Vansjø, a shallow nutrient-rich lake in southeastern Norway. To develop the model, we first identified controls on interannual variability in seasonally aggregated water quality. These variables were then included in a GBN, and conditional probability densities were fit using observations (≤39 years). GBN predictions had R2 values of 0.37 (chl a) to 0.75 (colour) and classification errors of 32 % (TP) to 17 % (cyanobacteria). For all but lake colour, including weather variables did not improve the predictive performance (assessed through cross-validation). Overall, we found the GBN approach to be well suited to seasonal water quality forecasting. It was straightforward to produce probabilistic predictions, including the probability of exceeding management-relevant thresholds. The GBN could be sensibly parameterised using only the observed data, despite the small dataset. Developing a comparable discrete BN was much more subjective and time-consuming. Although low interannual variability and high temporal autocorrelation in the study lake meant the GBN performed only slightly better than a seasonal naïve forecast (where the forecasted value is simply the value observed the previous growing season), we believe that the forecasting approach presented here could be particularly useful in areas with higher sensitivity to catchment nutrient delivery and seasonal climate and for forecasting at shorter (daily or monthly) timescales. Despite the parametric constraints of GBNs, their simplicity, together with the relative accessibility of BN software with GBN handling, means they are a good first choice for BN development with continuous variables.

show abstract

Semiparametric Bayesian networks for continuous data

Cited by 8 publications

References 21 publications

Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

Non-parametric Multivariate Kernel Regression Estimation to Describe Cognitive Processes and Mental Representations

Recursive and non-recursive regression estimators using Bernstein polynomials

Seasonal forecasting of lake water quality and algal bloom risk using a continuous Gaussian Bayesian network

Contact Info

Product

Resources

About