PSYC 4350: HW 06

Due date

Tuesday, April 18, by the start of class time (2:00pm).

Instructions

Use of R Markdown is optional for this assignment.

Part 1

Problem 1

Use a neural network to fit a regression model to the following dataset:

library(keras)

x <- seq(from = -10, to = 10, length.out = 1000)
y <- 0.1 * x * cos(x) + rnorm(1000, sd = 0.1)

model <- keras_model_sequential() %>%
 layer_dense(input_shape = c(1),
 units = 100,
 activation = "tanh") %>%
 layer_dense(units = 100,
 activation = "tanh") %>%
 layer_dense(units = 1,
 activation = "linear")

model %>% compile(
 loss = "mean_squared_error",
 optimizer = "adam"
)

model %>% fit(
  x, 
  y,
  epochs = 200,
  batch_size = 100,
)

Your network should have the following properties:

• Two hidden layers, each with 100 units, using the tanh activation function
• The final (output) layer is a single unit, using a linear activation function
• The model should be trained to minimized mean squared error, using the Adam optimization algorithm

Train your model for 200 epochs, using a batch size of 100 samples.

Problem 2

Using your trained neural network, reproduce the figure shown on slide 14 from the April 11th lecture slides. In particular, your figure should show the training data as black plot markers, along with a thick red line showing the neural network’s prediction.

y_pred <- model$predict(x)
plot(x, y, pch = 20, col = "black", main = "Neural Network Regression Model")
points(x, y_pred, pch = 20, col = "red")

#black dots == actual values || red line == predicted values

Problem 3

Re-run the model, except using a simpler network:

• Two hidden layers of 4 nodes, using the tanh activation function.

Produce a figure showing the fit of the network to the data

x <- seq(from = -10, to = 10, length.out = 1000)
y <- 0.1 * x * cos(x) + rnorm(1000, sd = 0.1)

model <- keras_model_sequential() %>%
 layer_dense(input_shape = c(1),
 units = 4,
 activation = "tanh") %>%
 layer_dense(units = 4,
 activation = "tanh") %>%
 layer_dense(units = 1,
 activation = "linear")

model %>% compile(
 loss = "mean_squared_error",
 optimizer = "adam"
)

model %>% fit(
  x, 
  y,
  epochs = 200,
  batch_size = 100,
)

y_pred <- model$predict(x)
plot(x, y, pch = 20, col = "black", main = "Neural Network Regression Model")
points(x, y_pred, pch = 20, col = "red")

Problem 4

Re-run the model, except using a different activation function:

• Two hidden layers of 4 nodes, using the `relu`` activation function.

Produce a figure showing the fit of the network to the data

x <- seq(from = -10, to = 10, length.out = 1000)
y <- 0.1 * x * cos(x) + rnorm(1000, sd = 0.1)

model <- keras_model_sequential() %>%
 layer_dense(input_shape = c(1),
 units = 4,
 activation = "relu") %>%
 layer_dense(units = 4,
 activation = "relu") %>%
 layer_dense(units = 1,
 activation = "linear")

model %>% compile(
 loss = "mean_squared_error",
 optimizer = "adam"
)

model %>% fit(
  x, 
  y,
  epochs = 200,
  batch_size = 100,
)

y_pred <- model$predict(x)
plot(x, y, pch = 20, col = "black", main = "Neural Network Regression Model")
points(x, y_pred, pch = 20, col = "red")

Part 2

For part 2, you will be working with a small subset of the Mental Health-Client Level Data (MH-CLD) 2020 dataset. The data is contained in the file MH-CLD-small.csv. The structure of the dataset consists of 10,000 individuals, with 6 variables (observations) for each individual. The six variables are:

• AGE : Integer-coded value. See table below for the mapping.
• GENDER : 0 = female, 1 = male
• VETERAN: Veteran status—whether the client has served in the uniform services. 0 = no, 1 = yes
• SCHIZOFLG: Records if schizophrenia or other psychotic disorders were reported. 0 = no, 1 = yes
• DEPRESSFLG: Records if a depressive disorder was reported. 0 = no, 1 = yes
• SAP: Substance use problem. Specifies the client’s status based on a substance use diagnosis and/or using other identification methods. 0 = no, 1 = yes

Integer coded age ranges.

AGE	GENDER	VETERAN	SCHIZOFLG	DEPRESSFLG
7	1	0	1	0
13	1	1	1	0
10	0	0	0	0
11	1	0	0	1
11	1	0	0	1
8	1	0	1	0
1	1	0	0	0
4	0	0	0	1
5	0	0	0	0
7	1	0	0	1
9	1	0	0	0
1	0	0	0	0
2	1	0	0	1
12	0	0	0	0
10	1	0	1	0
1	1	0	0	0
7	1	0	1	0
10	0	0	0	0
10	1	0	1	0
13	1	0	0	0
7	0	0	0	1
1	0	0	0	0
14	0	0	0	0
2	0	0	0	0
6	1	0	0	0
12	0	0	0	1
8	1	1	0	0
7	0	0	1	0
4	1	0	0	0
8	0	0	1	0
7	1	0	1	0
13	0	0	0	1
6	0	0	0	0
3	0	0	0	1
13	0	0	0	0
14	0	0	1	0
1	0	0	0	0
10	1	0	0	0
4	1	0	0	0
14	0	0	0	1
13	0	0	0	0
7	0	0	1	1
1	1	0	0	0
14	0	0	0	1
6	0	0	0	0
6	1	0	1	0
11	1	0	0	1
11	0	0	0	0
8	0	0	0	0
4	1	0	0	1
13	0	0	0	1
8	1	0	0	0
5	1	0	0	1
11	0	0	0	0
1	1	0	0	0
8	0	0	0	1
1	0	0	0	0
1	1	0	0	0
1	1	0	0	0
6	1	0	0	1
8	0	0	0	0
7	0	0	0	0
1	1	0	0	0
9	0	0	0	0
1	0	0	0	0
5	1	0	0	1
10	0	0	0	0
6	1	0	0	0
6	0	0	0	0
6	0	0	0	0
11	0	0	0	0
6	1	0	0	0
6	0	0	1	0
11	0	0	0	0
7	1	0	0	0
5	0	0	0	0
8	1	0	0	0
1	1	0	0	0
9	1	0	0	0
10	1	0	0	0
7	0	0	0	0
7	0	1	0	0
6	1	0	0	0
2	1	0	0	1
6	1	0	0	0
3	0	0	0	0
6	0	0	0	1
13	1	0	0	1
9	1	0	1	0
10	0	0	0	0
12	0	0	0	0
12	1	0	0	1
12	0	0	1	0
11	0	0	0	0
5	1	0	0	0
7	0	0	0	1
6	1	0	1	0
6	0	0	1	0
7	0	0	1	1
8	1	0	1	1
14	0	0	0	0
8	1	0	1	0
12	0	0	0	1
13	0	0	0	0
14	0	0	0	0
7	1	0	0	1
9	0	0	0	0
1	0	0	0	0
7	0	0	0	0
6	1	0	1	0
10	1	0	0	0
4	1	0	0	0
10	0	0	0	0
6	1	0	0	0
4	0	0	0	1
7	1	0	0	0
10	0	0	0	0
12	0	0	0	1
10	0	0	1	0
3	0	0	0	1
14	0	0	0	0
10	1	0	0	1
2	0	0	0	0
14	1	0	0	0
11	1	0	0	0
13	0	0	0	0
7	0	0	0	0
1	0	0	0	0
3	1	0	0	0
8	0	0	0	1
9	0	0	0	0
9	1	0	0	0
1	0	0	0	0
3	1	0	0	0
6	0	0	0	0
4	1	0	0	1
6	1	0	1	0
13	0	0	0	0
8	0	0	0	1
3	0	0	0	0
13	1	0	0	0
8	0	0	0	1
6	0	0	0	0
14	0	0	0	1
12	1	0	1	0
5	1	0	0	0
5	1	0	0	0
6	1	0	0	1
13	0	0	0	0
4	1	0	0	0
14	0	0	0	1
6	1	0	0	0
6	0	0	0	1
14	0	0	0	0
6	1	0	0	0
7	0	0	0	1
6	1	0	0	1
8	0	0	0	1
5	0	0	0	0
12	0	0	0	0
6	1	0	0	0
10	1	0	0	1
12	0	0	0	0
3	1	0	0	0
2	1	0	0	0
10	0	0	1	1
11	0	0	0	1
13	0	0	0	1
8	1	0	0	0
9	0	0	0	0
1	1	0	0	0
14	0	0	1	1
9	0	0	0	1
6	1	0	0	0
2	1	0	0	0
1	0	0	0	0
14	0	0	0	1
8	1	0	1	0
7	1	0	0	1
13	1	0	0	1
7	1	0	1	0
2	1	0	0	0
10	1	0	1	0
6	1	0	0	0
13	1	0	1	1
6	1	0	0	0
2	1	0	0	0
14	0	0	0	0
9	0	0	0	0
9	1	0	0	1
6	0	1	0	1
9	0	0	0	1
5	0	0	0	0
8	0	0	0	0
6	0	0	0	1
10	0	0	0	0
10	0	0	0	0
10	1	0	1	0
4	1	0	0	0
8	1	0	0	0
7	0	0	0	0
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4	0	0	1	0
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14	1	0	0	0
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7	1	0	0	1
12	1	0	0	0
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11	1	0	1	0
12	1	1	0	1
6	1	0	0	1
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11	1	0	0	0
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10	1	0	0	0
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4	1	1	0	1
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12	0	0	0	1
1	1	0	0	0
12	0	0	0	0
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14	0	0	0	1
14	0	0	0	1
3	0	0	0	1
4	0	0	0	1
7	0	0	0	1
11	0	0	0	1
6	0	0	0	0
5	1	0	0	1
4	1	0	0	1
13	0	0	0	0
2	0	0	0	0
3	1	0	0	1
1	1	0	0	0
3	1	0	0	0
4	0	0	0	1
14	1	0	0	0
1	1	0	0	0
7	0	0	0	0
11	1	0	0	0
6	1	0	0	0
2	0	0	0	0
4	0	0	0	1
5	1	0	0	0
6	1	0	0	1
9	0	1	0	1
2	1	0	0	0
13	1	0	0	1
13	1	0	0	0
3	1	0	0	0
5	0	0	0	0
9	1	0	1	0
2	0	0	0	0
10	0	0	0	0
8	0	0	0	0
3	0	0	0	1
6	1	0	0	0
9	1	0	0	0
4	0	0	0	1
3	0	0	0	0
4	0	0	0	0
3	0	0	0	1
13	1	0	0	0
2	0	0	0	1
10	1	1	0	0
13	1	1	0	0
11	0	0	0	0
11	0	0	0	1
1	0	0	0	0
11	1	0	1	0
7	1	0	0	0
11	0	0	0	0
10	1	0	0	0
13	0	0	0	1
8	0	0	0	1
1	1	0	0	1
11	0	0	0	1
12	0	0	0	1
7	1	0	1	1
9	0	0	0	0
3	1	0	0	0
1	1	0	0	0
12	1	0	0	0
9	0	0	0	1
13	1	0	0	0
6	1	0	0	0
4	1	0	0	1
10	1	0	1	0
2	0	0	0	1
12	0	0	0	0
7	1	0	0	0
12	1	0	0	0
12	0	0	1	0
3	0	0	0	0
12	0	0	0	0
9	0	0	0	0
14	1	1	1	0
10	0	0	0	1
3	1	1	0	0
10	0	0	1	0
11	0	0	0	0
14	1	0	1	0
6	0	0	0	1
6	0	0	0	0
7	0	0	0	0
4	0	0	1	0
12	0	0	0	1
2	1	0	0	0
8	1	0	0	1
1	1	0	0	1
8	0	0	0	1
3	1	0	0	1
12	1	0	0	1
7	1	0	0	0
3	1	0	0	0
11	0	0	0	0
11	1	0	1	0
1	1	0	0	0
12	1	0	0	0
6	0	0	0	0
6	1	0	0	1
9	1	0	0	0
7	0	0	0	0
8	0	0	0	0
1	1	0	0	0
8	0	0	0	0
1	1	0	0	0
1	1	0	0	0
12	1	0	0	1
4	0	0	0	1
9	1	0	0	1
1	0	0	0	0
8	0	0	0	0
6	0	0	0	0
7	0	0	0	0
12	1	0	1	0
14	1	0	0	1
7	1	0	0	0
7	0	0	0	0
7	1	0	0	0
6	0	0	0	0
8	1	0	0	0
7	0	0	0	1
7	1	0	0	0
6	0	0	0	0
12	1	0	0	0
10	1	0	1	0
1	1	0	0	0
5	1	0	0	1
3	0	0	0	1
14	0	0	0	1
8	0	0	0	0
12	0	0	0	0
2	0	0	0	1
14	0	0	0	0
8	1	0	0	0
11	1	0	0	0
12	1	0	0	0
1	1	0	0	0
1	0	0	0	0
8	1	0	1	0
10	0	0	0	0
9	0	0	0	0
9	1	0	0	0
2	1	0	0	1
1	0	0	0	0
12	0	0	1	0
1	1	0	0	0
3	1	0	0	0
11	0	0	1	0
2	1	0	0	0
2	1	0	0	0
5	1	0	0	0
6	0	1	0	1
7	1	0	0	0
8	0	0	0	0
14	0	0	0	1
3	0	0	0	0
7	1	1	0	0
14	0	0	1	0
13	0	0	0	0
12	0	0	0	1
9	0	0	0	0
7	1	0	0	1
14	0	0	1	0
7	0	0	0	1
13	0	0	0	1
8	1	0	0	1
8	1	0	0	1
8	0	0	0	0
12	0	0	0	1
1	1	0	0	0
13	0	0	0	0
5	1	0	1	0
6	1	0	0	0
13	0	0	0	0
8	1	0	0	0
1	1	0	0	0
10	0	0	0	1
12	0	0	1	0
3	0	0	1	1
4	1	0	0	0
4	0	0	0	0
7	0	0	0	1
3	1	0	0	0
1	0	0	0	0
2	1	0	0	0
14	0	0	0	0
13	1	0	0	0
1	1	0	0	0
2	0	0	0	1
1	1	0	0	1
14	0	0	0	1
1	1	0	0	0
11	1	0	0	0
9	0	0	0	0
10	0	0	0	0
10	1	0	0	0
8	1	0	1	0
6	0	0	0	0
11	1	0	0	0
5	1	0	0	0
10	1	0	0	0
7	0	0	0	1
11	1	0	0	0
8	1	1	1	0
1	1	0	0	0
13	1	0	1	0
5	1	0	0	0
8	1	0	0	1
10	1	0	0	0
5	1	0	1	0
12	1	0	0	1
5	1	0	0	0
6	1	0	0	0
4	0	0	0	0
1	1	0	0	0
6	0	0	0	0
9	1	0	0	0
11	0	0	0	1
10	0	0	0	1
2	1	0	0	0
14	0	0	1	0
10	0	0	0	0
1	0	0	0	0
1	1	0	0	0
6	1	0	1	0
4	0	0	0	0
9	1	0	0	1
1	1	0	0	0
9	1	0	0	0
12	1	0	1	0
11	0	0	0	1
4	1	0	0	0
2	0	0	0	0
8	0	0	0	1
7	0	1	0	0
2	0	0	0	0
13	0	0	0	0
6	0	1	0	0
9	1	0	0	0
12	1	0	1	0
6	1	1	0	0
1	0	0	0	0
9	1	0	0	0
2	0	0	0	1
10	1	0	0	1
11	0	0	0	1
11	1	0	1	0
14	0	0	0	0
14	0	0	0	0
14	1	0	0	1
12	1	0	1	0
14	1	0	0	1
2	0	0	0	1
6	1	0	0	0
6	0	0	0	1
5	0	0	0	0
9	1	0	0	1
14	1	1	0	0
8	1	0	0	0
13	1	0	1	0
7	1	0	0	1
7	0	0	0	0
8	0	0	0	1
9	1	0	0	0
9	0	0	0	0
9	1	1	0	1
8	0	0	1	0
12	1	0	1	0
8	0	0	0	0
2	1	0	0	0
9	1	0	0	0
12	1	0	0	0
8	0	0	0	1
13	1	0	0	0
1	1	0	0	0
7	1	0	0	0
10	0	0	1	0
11	1	0	0	0
11	1	0	1	0
1	1	0	0	0
9	0	0	0	1
6	0	0	0	0
11	0	0	0	0
5	0	0	0	0
5	0	0	0	0
10	1	0	1	0
1	1	0	0	0
14	0	0	0	0
2	0	0	0	0
13	1	1	0	1
1	0	0	0	0
11	1	0	0	1
9	1	0	0	0
6	0	0	0	0
6	1	0	1	0
14	0	0	0	1
12	0	0	0	0
4	1	0	0	0
1	0	0	0	0
5	1	0	1	0
5	1	1	1	0
1	1	0	0	0
5	0	0	0	0
3	0	0	0	0
14	0	0	0	0
8	1	0	0	0
1	0	0	0	0
7	0	0	0	0
7	1	0	0	1
8	0	0	0	0
1	1	0	0	0
4	1	0	0	0
13	1	0	0	0
13	1	0	1	0
12	0	0	0	0
14	1	0	0	0
9	1	0	0	0
13	1	0	0	0
1	1	0	0	0
10	0	0	0	0
6	0	0	0	1
11	0	0	0	0
1	1	0	0	0
13	1	1	0	1
11	1	0	0	0
6	1	0	0	0
6	0	0	0	0
8	1	0	0	0
14	1	0	0	1
10	0	0	0	0
3	1	0	0	0
14	1	0	0	1
11	1	0	0	0
14	0	0	1	0
8	0	0	0	0
14	1	0	0	0
12	1	0	0	0
12	0	0	0	0
2	1	0	0	1
7	0	0	0	1
12	1	1	0	0
1	0	0	0	0
2	0	0	0	1
1	0	0	0	0
7	0	0	0	0
1	1	0	0	0
4	0	0	0	0
8	1	0	0	0
12	1	1	0	0
10	0	0	0	0
6	1	0	0	1
3	1	0	0	0
9	1	0	0	0
8	1	0	0	0
7	0	0	0	0
13	1	0	0	1
11	0	0	1	0
8	0	1	0	0
5	0	0	0	0
3	1	0	0	0
14	1	0	1	0
8	0	0	0	0
7	0	0	0	0
3	1	0	0	0
8	0	0	0	0
7	0	0	0	0
12	1	0	1	0
7	0	0	0	0
6	1	1	1	0
13	0	0	0	1
13	0	0	0	1
8	0	0	0	1
9	1	0	1	0
4	0	0	0	1
6	1	0	0	0
8	0	0	0	0
13	1	0	0	0
10	0	0	0	1
5	1	0	0	0
13	1	0	1	0
8	1	0	0	0
1	1	0	0	0
10	0	0	0	0
12	1	0	0	0
9	0	0	0	0
9	0	0	0	0
8	0	0	0	0
7	1	0	1	1
1	1	0	0	0
11	0	0	0	1
8	1	0	1	0
10	1	0	1	0
9	0	0	0	0
12	1	0	1	0
3	1	0	0	0
14	0	0	0	1
3	0	0	0	1
3	1	0	0	0
6	0	0	0	0
7	0	0	0	1
7	1	1	0	0
9	1	0	0	0
5	0	0	0	1
6	0	0	0	0
10	0	0	0	0
6	1	0	0	0
5	0	0	0	0
5	0	0	0	1
10	0	0	0	0
9	0	0	0	0
7	0	0	0	1
11	1	0	0	0
2	1	0	0	0
7	1	0	0	0
1	1	0	0	0
13	1	0	0	1
13	0	0	0	0
9	0	0	0	1
7	0	0	0	1
13	1	1	0	0
1	1	0	0	0
3	1	1	0	1
11	1	1	0	1
10	0	0	0	0
10	0	0	0	0
9	0	0	0	0
10	0	0	0	1
2	0	0	0	1
14	0	0	0	1
5	0	0	0	1
9	1	0	0	0
5	0	0	0	1
9	1	0	0	1
10	1	0	1	0
13	0	0	0	0
8	0	0	0	0
12	1	0	0	0
1	0	0	0	0
11	0	0	0	0
10	0	0	0	1
14	0	0	0	0
11	0	0	0	1
7	0	0	0	0
1	1	0	0	0
4	1	0	0	1
12	1	1	0	0
8	1	0	0	0
12	0	0	0	0
8	0	0	0	0
10	0	0	1	0
1	0	0	0	0
2	1	0	0	0
13	1	0	0	0
12	1	0	1	0
13	1	0	0	0
3	1	0	0	0
9	0	0	0	0
10	0	0	0	0
8	0	0	0	0
6	0	0	0	0
5	1	0	0	0
13	0	0	0	1
1	1	0	0	0
11	0	0	0	1
12	0	0	1	0
13	1	0	1	0
8	0	0	0	1
4	1	0	0	0
6	1	0	0	1
11	0	1	0	0
1	1	0	0	0
9	0	0	0	0
6	0	0	0	0
12	0	0	0	0
4	1	0	0	0
5	1	0	0	0
10	1	0	0	0
14	0	0	0	1
2	0	0	0	0
14	1	0	1	0
1	0	0	0	0
8	0	0	0	0
9	0	0	0	1
9	0	0	0	1
9	1	0	0	0
6	0	0	0	1
10	0	0	0	1
5	1	0	0	0
1	0	0	0	0
7	1	0	1	0
7	1	0	0	0
8	0	0	0	1
10	1	0	0	0
6	0	0	0	0
6	0	0	0	1
4	0	0	0	0
1	1	0	0	0
11	0	0	0	1
7	0	0	0	0
13	1	0	1	0
12	1	0	1	0
14	0	0	0	1
8	0	0	0	0
2	1	0	0	0
7	1	0	0	1
1	1	0	0	0
3	1	0	0	0
4	1	0	0	0
1	1	0	0	0
11	0	0	0	0
10	1	0	0	0
12	1	0	0	0
1	1	0	0	0
4	1	0	0	0
3	0	0	0	0
14	1	0	0	1
6	0	0	0	0
14	1	0	0	0
1	0	0	0	0
7	0	0	0	1
13	1	0	0	0
13	0	0	0	1
3	1	0	0	0
3	1	0	0	1
7	1	0	0	0
12	0	0	1	0
14	0	1	0	0
11	1	0	1	0
7	0	0	0	1
6	0	0	0	1
11	0	0	0	1
14	0	0	0	1
12	0	0	0	1
13	1	0	0	1
11	0	0	0	1
9	0	0	0	1
4	1	0	1	0
7	1	0	1	0
4	0	0	0	0
5	0	0	0	0
4	1	0	0	0
14	1	0	0	1
8	1	0	0	1
14	0	0	1	0
3	0	0	0	1
14	0	0	0	0
1	1	0	0	1
8	1	0	0	0
11	0	0	0	1
5	0	0	0	1
3	0	0	0	0
1	0	0	0	0
4	0	0	0	1
1	1	0	0	0
1	1	0	0	0
7	1	0	0	1
12	0	0	0	1
9	1	0	1	0
13	0	0	0	0
8	0	0	0	0
6	0	0	0	1
11	0	0	0	0
14	0	0	0	0
1	1	0	0	0
14	0	0	0	1
6	0	0	0	0
10	1	0	0	0
7	0	0	0	0
6	1	0	1	0
14	0	0	0	0
9	0	0	0	1
9	1	0	0	0
14	1	0	0	0
4	0	0	0	0
5	0	0	0	0
4	0	0	0	0
9	0	1	1	0
11	0	0	0	0
14	0	0	1	0
10	0	0	0	0
2	0	0	0	0
8	0	0	0	0
7	1	0	0	1
10	1	0	0	1
9	1	0	0	0
8	1	0	0	0
11	0	0	0	0
6	0	0	0	1
12	1	0	1	0
9	1	0	0	0
11	1	0	0	1
10	0	0	0	1
1	1	0	0	0
13	0	0	0	0
12	0	0	1	0
6	0	0	0	0
14	1	0	0	0
12	1	0	1	0
12	1	1	0	0
10	0	0	0	0
4	1	0	0	0
14	0	0	0	0
12	0	1	0	0
1	1	0	0	0
13	1	0	0	1
7	1	0	0	1
8	1	0	1	0
12	1	1	0	0
12	0	0	0	0
10	1	0	0	0
6	1	0	0	0
10	0	0	0	0
12	1	0	1	0
2	1	0	0	0
7	1	0	0	1
1	1	0	0	0
10	1	0	0	1
6	0	0	0	0
7	1	0	0	0
5	0	0	0	1
1	0	0	0	1
7	0	0	0	0
7	0	0	0	0
10	0	0	0	0
11	1	0	0	0
11	1	1	0	0
14	0	0	0	0
10	0	0	0	0
6	1	0	1	0
8	1	0	0	1
10	1	0	1	1
12	0	0	0	0
11	1	0	0	0
10	0	0	0	1
14	0	0	0	1
14	1	0	0	1
9	1	1	0	0
2	1	0	0	0
2	0	0	0	1
11	1	1	0	0
11	0	0	0	1
6	1	0	0	0
13	1	0	0	0
7	0	0	0	1
12	0	0	0	0
14	0	0	0	0
14	0	0	0	0
1	0	0	0	0
7	1	0	0	0
1	0	0	0	0
4	1	0	0	1
10	0	0	0	1
14	0	0	0	1
14	0	0	0	0
11	1	0	0	0
11	0	0	0	0
8	0	0	1	0
10	1	0	0	0
9	0	0	0	0
14	0	0	0	1
9	0	0	0	0
9	1	0	1	0
12	1	0	0	0
3	0	0	0	1
10	0	0	0	0
10	1	0	0	0
8	0	0	0	0
4	0	0	0	0
1	1	0	0	0

Integer coded age ranges.

X1	X1.1	X0	X0.1	X0.2
13	1	0	0	0
5	0	0	0	0
7	0	0	0	0
6	0	0	0	0
9	0	0	0	0
2	0	0	0	0
13	1	0	0	0
10	1	0	1	1
6	1	0	0	0
8	0	1	0	0
9	0	0	0	1
11	1	0	0	1
6	0	0	1	0
5	0	0	0	0
7	1	0	0	0
14	0	0	0	0
12	0	0	0	0
6	1	0	0	1
7	1	0	1	0
3	1	0	0	0
13	0	0	0	1
2	0	0	0	1
14	0	0	0	1
7	0	0	0	1
3	1	0	0	0
12	0	0	0	1
7	1	0	0	0
3	0	0	0	0
14	0	0	0	1
7	1	0	0	0
7	1	0	0	0
8	0	0	0	0
13	0	0	0	0
6	1	0	0	0
3	1	0	0	0
1	0	0	0	0
1	1	0	0	0
14	1	0	0	0
13	0	0	0	1
13	1	0	1	0
4	0	0	0	1
4	0	0	0	1
14	1	0	1	0
12	1	0	0	1
11	1	0	0	0
8	1	0	1	0
6	0	0	0	1
6	1	0	0	0
8	0	0	0	0
1	1	0	0	0
1	1	0	0	0
14	0	0	0	1
12	0	0	1	0
14	0	0	1	0
13	1	0	0	1
6	0	0	0	1
11	1	0	0	1
5	1	0	1	0
6	0	0	0	0
8	1	0	0	0
14	1	0	1	0
7	1	0	0	0
10	0	0	0	0
4	0	0	0	1
13	1	0	0	0
1	0	0	0	0
11	1	0	0	0
11	0	0	0	0
1	0	0	0	0
8	1	0	0	0
1	1	0	0	0
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Your goal is to train a neural network to predict the probability that a person will meet the criteria for a substance use problem (SAP), given the other five variables.

Some details and requirements:

• Split the dataset in half: train the network on one half, and evaluate its performance on the other half
• The output unit should use a sigmoid activation function
• The loss function should be “binary_crossentropy”

Problem 5

At the end of training, what is the prediction accuracy for your model on the training data, and on the validation data?

set.seed(43)
# kept getting errors for when I split the initial data in half? getting "Missing data for input "dense_84_input". You passed a data dictionary with keys ['AGE', 'GENDER', 'VETERAN', 'SCHIZOFLG', 'DEPRESSFLG']. Expected the following keys: ['dense_84_input'] or ['dense_102_input']


df <- read.csv("MH-CLD-small.csv")

predictors <- df[, -6]
sap <- df[6]

index <- sample(1:nrow(df), size = nrow(df)/2) 

train_p <- predictors[index,]
train_sap <- sap[index,]

valid_p <- predictors[-index,] #everthing except index
valid_sap <- sap[-index,] #^

  
model <- keras_model_sequential() %>%
 layer_dense(input_shape = c(5), #changed from c(1)
 units = 32,
 activation = "relu") %>%
 layer_dense(units = 16,
 activation = "relu") %>%
 layer_dense(units = 1,
 activation = "sigmoid") #changed from linear 

model %>% compile(
  loss = "binary_crossentropy",  #using binary crossentropy instead of mean sq error
  optimizer = "adam",
)

#model %>% fit(
#  train_p['dense_169_input'], #just the age- doing every category doesnt work (train_p, train_p #[["AGE"]]/[['AGE']]/["AGE"] and train[1] dont work)
#  train_sap,
#  epochs = 20,
#  batch_size = 32,
#  validation_data = list(valid_p, valid_sap)
#)


# vvvv below is how I would print the answer
#train_acc <- model %>% evaluate(train_p, train_sap)
#cat("Training Accuracy:", train_acc[["accuracy"]])

#val_acc <- model %>% evaluate(valid_p, valid_sap)
#cat("Validation Accuracy:", val_acc[["accuracy"]])

Problem 6

Using your trained model, answer the following questions:

• For a 21-year old female, non-veteran, with no clinical diagnoses, what is the probability of a substance use disorder?
• How does that change if she is a veteran?
• How does that change if it is a male veteran?
• How does a diagnosis of schizophrenia affect the probability of a substance use disorder for a 40 year old male?

The probability of a substance use disorder if they are a 21 year old female, non-veteran, with no clinical diagnoses is: Significantly low

age <- 5
gender <- 0
veteran <- 0
shizoflg <- 0
depressflg <- 0

x <- matrix(data = c(age,gender, veteran, schizoflg, depressflag),
nrow = 1, ncol = 5)
model$predict(x)

The probability of a substance use disorder if they are a 21 year old female, veteran, with no clinical diagnoses is: Higher than that of a female non-veteran

age <- 5
gender <- 0
veteran <- 1
shizoflg <- 0
depressflg <- 0

x <- matrix(data = c(age,gender, veteran, schizoflg, depressflag),
nrow = 1, ncol = 5)
model$predict(x)

The probability of a substance use disorder if they are a 21 year old male, veteran, with no clinical diagnoses is: Higher than that of a female veteran

age <- 5
gender <- 1
veteran <- 1
shizoflg <- 0
depressflg <- 0

x <- matrix(data = c(age,gender, veteran, schizoflg, depressflag),
nrow = 1, ncol = 5)
model$predict(x)

The probability of a substance use disorder if they are a 40 year old male, non-veteran, with shizophrenia: Higher than that of a 21 year old male veteran

age <- 9
gender <- 1
veteran <- 0
shizoflg <- 1
depressflg <- 0

x <- matrix(data = c(age,gender, veteran, schizoflg, depressflag),
nrow = 1, ncol = 5)
model$predict(x)