AI News, Fitting a Neural Network in R; neuralnet package

Fitting a Neural Network in R; neuralnet package

Neural networks have always been one of the fascinating machine learning models in my opinion, not only because of the fancy backpropagation algorithm but also because of their complexity (think of deep learning with many hidden layers) and structure inspired by the brain.

Neural networks have not always been popular, partly because they were, and still are in some cases, computationally expensive and partly because they did not seem to yield better results when compared with simpler methods such as support vector machines (SVMs).

sum(is.na(x))) crim zn indus chas nox rm age dis rad tax ptratio

0 0 0 0 0 0 0 0 0 0 0 black lstat medv

0 0 0 There is no missing data, good.

We proceed by randomly splitting the data into a train and a test set, then we fit a linear regression model and test it on the test set.

index <- sample(1:nrow(data),round(0.75*nrow(data))) train <- data[index,] test <- data[-index,] lm.fit <- glm(medv~., data=train) summary(lm.fit) pr.lm <- predict(lm.fit,test) MSE.lm <- sum((pr.lm - test$medv)^2)/nrow(test) The sample(x,size) function simply outputs a vector of the specified size of randomly selected samples from the vector x.

Update: We published another post about Network analysis at DataScience+ Network analysis of Game of Thrones In this post, we are going to fit a simple neural network using the neuralnet package and fit a linear model as a comparison.

We proceed by randomly splitting the data into a train and a test set, then we fit a linear regression model and test it on the test set.

I cannot emphasize enough how important this step is: depending on your dataset, avoiding normalization may lead to useless results or to a very difficult training process (most of the times the algorithm will not converge before the number of maximum iterations allowed).

As far as the number of neurons is concerned, it should be between the input layer size and the output layer size, usually 2/3 of the input size.

The input layer has 13 inputs, the two hidden layers have 5 and 3 neurons and the output layer has, of course, a single output since we are doing regression. Let’s

fit the net: The neuralnet package provides a nice tool to plot the model: This is the graphical representation of the model with the weights on each connection:

The black lines show the connections between each layer and the weights on each connection while the blue lines show the bias term added in each step.

pr.nn <- compute(nn,test_[,1:13]) pr.nn_ <- pr.nn$net.result*(max(data$medv)-min(data$medv))+min(data$medv) test.r <- (test_$medv)*(max(data$medv)-min(data$medv))+min(data$medv) MSE.nn <- sum((test.r - pr.nn_)^2)/nrow(test_) we then compare the two MSEs print(paste(MSE.lm,MSE.nn))

visually inspecting the plot we can see that the predictions made by the neural network are (in general) more concetrated around the line (a perfect alignment with the line would indicate a MSE of 0 and thus an ideal perfect prediction) than those made by the linear model. plot(test$medv,pr.nn_,col='red',main='Real

I am also initializing a progress bar using the plyr library because I want to keep an eye on the status of the process since the fitting of the neural network may take a while. set.seed(450)

cv.error 10.32697995 17.640652805 6.310575067 15.769518577 5.730130820 10.520947119 6.121160840 6.389967211 8.004786424 17.369282494 9.412778105 The code for the box plot: boxplot(cv.error,xlab='MSE

visually inspecting the plot we can see that the predictions made by the neural network are (in general) more concetrated around the line (a perfect alignment with the line would indicate a MSE of 0 and thus an ideal perfect prediction) than those made by the linear model.

While there are different kind of cross validation methods, the basic idea is repeating the following process a number of time: Then by calculating the average error we can get a grasp of how the model is doing.

Network model

While the hierarchical database model structures data as a tree of records, with each record having one parent record and many children, the network model allows each record to have multiple parent and child records, forming a generalized graph structure.

This property applies at two levels: the schema is a generalized graph of record types connected by relationship types (called 'set types' in CODASYL), and the database itself is a generalized graph of record occurrences connected by relationships (CODASYL 'sets').

Until the early 1980s the performance benefits of the low-level navigational interfaces offered by hierarchical and network databases were persuasive for many large-scale applications, but as hardware became faster, the extra productivity and flexibility of the relational model led to the gradual obsolescence of the network model in corporate enterprise usage.

Social and Economic Networks: Models and Analysis

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course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks.

Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids.

3.6: Block Models

Learn how to model social and economic networks and their impact on human behavior.

course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks.

Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids.

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