# Learning Bayesian Models With R.pdf

In statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone.[1][2][3]Unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.

## Learning Bayesian Models with R.pdf

Supervised learning algorithms perform the task of searching through a hypothesis space to find a suitable hypothesis that will make good predictions with a particular problem.[4] Even if the hypothesis space contains hypotheses that are very well-suited for a particular problem, it may be very difficult to find a good one. Ensembles combine multiple hypotheses to form a (hopefully) better hypothesis. The term ensemble is usually reserved for methods that generate multiple hypotheses using the same base learner.[according to whom?]The broader term of multiple classifier systems also covers hybridization of hypotheses that are not induced by the same base learner.[citation needed]

Empirically, ensembles tend to yield better results when there is a significant diversity among the models.[5][6] Many ensemble methods, therefore, seek to promote diversity among the models they combine.[7][8] Although perhaps non-intuitive, more random algorithms (like random decision trees) can be used to produce a stronger ensemble than very deliberate algorithms (like entropy-reducing decision trees).[9] Using a variety of strong learning algorithms, however, has been shown to be more effective than using techniques that attempt to dumb-down the models in order to promote diversity.[10] It is possible to increase diversity in the training stage of the model using correlation for regression tasks [11] or using information measures such as cross entropy for classification tasks.[12]

The question with any use of Bayes' theorem is the prior, i.e., the probability (perhaps subjective) that each model is the best to use for a given purpose. Conceptually, BMA can be used with any prior. R packages ensembleBMA[20] and BMA[21] use the prior implied by the Bayesian information criterion, (BIC), following Raftery (1995).[22] R package BAS supports the use of the priors implied by Akaike information criterion (AIC) and other criteria over the alternative models as well as priors over the coefficients.[23]

A "bucket of models" is an ensemble technique in which a model selection algorithm is used to choose the best model for each problem. When tested with only one problem, a bucket of models can produce no better results than the best model in the set, but when evaluated across many problems, it will typically produce much better results, on average, than any model in the set.

Gating is a generalization of Cross-Validation Selection. It involves training another learning model to decide which of the models in the bucket is best-suited to solve the problem. Often, a perceptron is used for the gating model. It can be used to pick the "best" model, or it can be used to give a linear weight to the predictions from each model in the bucket.

When a bucket of models is used with a large set of problems, it may be desirable to avoid training some of the models that take a long time to train. Landmark learning is a meta-learning approach that seeks to solve this problem. It involves training only the fast (but imprecise) algorithms in the bucket, and then using the performance of these algorithms to help determine which slow (but accurate) algorithm is most likely to do best.[30]

Stacking typically yields performance better than any single one of the trained models.[32] It has been successfully used on both supervised learning tasks (regression,[33] classification and distance learning [34]) and unsupervised learning (density estimation).[35] It has also been used to estimate bagging's error rate.[3][36] It has been reported to out-perform Bayesian model-averaging.[37] The two top-performers in the Netflix competition utilized blending, which may be considered a form of stacking.[38]

Land cover mapping is one of the major applications of Earth observation satellite sensors, using remote sensing and geospatial data, to identify the materials and objects which are located on the surface of target areas. Generally, the classes of target materials include roads, buildings, rivers, lakes, and vegetation.[45] Some different ensemble learning approaches based on artificial neural networks,[46] kernel principal component analysis (KPCA),[47] decision trees with boosting,[48] random forest[45] and automatic design of multiple classifier systems,[49] are proposed to efficiently identify land cover objects.

Classification of malware codes such as computer viruses, computer worms, trojans, ransomware and spywares with the usage of machine learning techniques, is inspired by the document categorization problem.[54] Ensemble learning systems have shown a proper efficacy in this area.[55][56]

While speech recognition is mainly based on deep learning because most of the industry players in this field like Google, Microsoft and IBM reveal that the core technology of their speech recognition is based on this approach, speech-based emotion recognition can also have a satisfactory performance with ensemble learning.[63][64]

Fraud detection deals with the identification of bank fraud, such as money laundering, credit card fraud and telecommunication fraud, which have vast domains of research and applications of machine learning. Because ensemble learning improves the robustness of the normal behavior modelling, it has been proposed as an efficient technique to detect such fraudulent cases and activities in banking and credit card systems.[68][69]

First and foremost, this book provides a practical introduction to how to use these specific R packages to create models. We focus on a dialect of R called the tidyverse that is designed with a consistent, human-centered philosophy, and demonstrate how the tidyverse and the tidymodels packages can be used to produce high quality statistical and machine learning models.

After that, this book is separated into parts, starting with the basics of modeling with tidy data principles. Chapters 4 through 9 introduces an example data set on house prices and demonstrates how to use the fundamental tidymodels packages: recipes, parsnip, workflows, yardstick, and others.

This book is not intended to be a comprehensive reference on modeling techniques; we suggest other resources to learn more about the statistical methods themselves. For general background on the most common type of model, the linear model, we suggest Fox (2008). For predictive models, M. Kuhn and Johnson (2013) and M. Kuhn and Johnson (2020) are good resources. For machine learning methods, Goodfellow, Bengio, and Courville (2016) is an excellent (but formal) source of information. In some cases, we do describe the models we use in some detail, but in a way that is less mathematical, and hopefully more intuitive.

On the applied side of reseach I am engaged in large scale machine learning modelling with NHS Scotland via a Programme Fellowship at the Alan Turing Institute, the UK's national institute for data science and AI. I am project lead for SPARRA (Scottish Patients At Risk of Re-admission and Admission), which is developing the next generation of a model designed to aid GPs in prioritising primary care interventions to reduce the risk of emergency hospital admissions. This work utilises various Electronic Health Records (EHRs) for roughly 3.6 million people in Scotland (roughly 80% population coverage).

Bayesian networks (BNs; Pearl 1988) are a class of graphical models defined over a set of random variables \(\mathbf X= \X_1, \ldots , X_N\\), each describing some quantity of interest, that are associated with the nodes of a directed acyclic graph (DAG) \(\mathcal G\). (They are often referred to interchangeably.) Arcs in \(\mathcal G\) express direct dependence relationships between the variables in \(\mathbf X\), with graphical separation in \(\mathcal G\) implying conditional independence in probability. As a result, \(\mathcal G\) induces the factorisation

Structure learning via score maximisation is performed using general-purpose optimisation techniques, typically heuristics, adapted to take advantage of these properties to increase the speed of structure learning. The most common are greedy search strategies that employ local moves designed to affect only few local distributions, to that new candidate DAGs can be scored without recomputing the full \(\text P(\mathcal D\text \mathcal G)\). This can be done either in the space of the DAGs with hill climbing and tabu search (Russell and Norvig 2009), or in the space of the equivalence classes with Greedy Equivalent Search (GES; Chickering 2002). Other options that have been explored in the literature are genetic algorithms (Larranaga et al. 1996) and ant colony optimisation (Campos et al. 2002). Exact maximisation of \(\text P(\mathcal D\text \mathcal G)\) and BIC has also become feasible for small data sets in recent years thanks to increasingly efficient pruning of the space of the DAGs and tight bounds on the scores (Cussens 2012; Suzuki 2017; Scanagatta et al. 2015).

In addition, we note that it is also possible to perform structure learning using conditional independence tests to learn conditional independence constraints from \(\mathcal D\), and thus identify which arcs should be included in \(\mathcal G\). The resulting algorithms are called constraint-based algorithms, as opposed to the score-based algorithms we introduced above; for an overview and a comparison of these two approaches see Scutari and Denis (2014). Chickering et al. (2004) proved that constraint-based algorithms are also NP-hard for unrestricted DAGs; and they are in fact equivalent to score-based algorithms given a fixed topological ordering when independence constraints are tested with statistical tests related to cross-entropy (Cowell 2001). For these reasons, in this paper we will focus only on score-based algorithms while recognising that a similar investigation of constraint-based algorithms represents a promising direction for future research. 041b061a72