I have a dataset (n=298), and I am currently working on a general additive model for it. There are three predictor variables and one response variable. I used this code to generate the GAM and perform leave one out cross validation:
ctrl <- trainControl(method = "LOOCV")
model <- train(response~ predictor1+ predictor2 + predictor3, data= data[2:5], method = "gam", trControl = ctrl)
While I think this worked in generating the model and performing cross validation, I'd like to graph the CV value over the degrees of freedom, similar to what is shown in the book image below. I'm not really sure how to go about this with my model as I am pretty new to using R.
[Graph Example
I tried to use plot(model), but it just outputs the graph below, which isn't very helpful and certainly isn't what I'm looking for. Any advice on how to approach this would be greatly appreciated. Thanks.
plot(model) Graph
Related
I am beginner in using R. I want to run a binary logistic regression and I guess some variables have nonlinearities. So I want to use splines method to understand affect of each range in a continuous variable. I am confused about it.
How can I do it in R ?
Knots (cut points) will determine automatically or I should determine manually ?
How can I know overall p-value of variable ?
model<- lrm(formula = PA ~ rcs(HEIGHT) + SLOPE + ASPECT, data=data, x=TRUE, y=TRUE)
I do not know "rcs" is helpful or not.. I found it by searching here. I will grateful if you guide me about it.
I am having some trouble reconciling my FFT results from MATLAB and TF. The results are actually very different. Here is what I have done:
1). I would attach my data file here but didn't find a way to do so. Anyways, my data is stored in a .mat file, and the variable we will work with is called 'TD'. In MATLAB, I first subtract the mean of the data, and then perform fft:
f_hat = TD-mean(TD);
x = fft(f_hat);
2). In TF, I use
tf.math.reduce_mean
to calculate the mean, and it only differs from MATLAB's mean on the order of 10^-8. So in TF I have:
mean_TD = tf.reduce_mean(TD)
f_hat_int = TD - mean_TD
f_hat_tf = tf.dtypes.cast(f_hat_int,tf.complex64)
x_tf = tf.signal.fft(f_hat_tf)
So up until 'f_hat' and 'f_hat_tf', the difference is very slight and is caused only by the difference in the mean. However, x and x_tf are very different. I am wondering did I not use TF's FFT correctly?
Thanks!
Picture showing the difference
I am attempting to modify and implement googles pattern of the Asynchronous Advantage Actor Critic (A3C) model. There are plenty of examples online out there that have gotten me started but I am running into a issues attempting to expand the samples.
All of the examples I can find focus on pong as the example which has a state based output of left or right or stay still. What I am trying to expand this to is a system that also has a separate on off output. In the context of pong, it would be a boost to your speed.
The code I am basing my code on can be found here. It is playing doom, but it still has the same left and right but also a fire button instead of stay still. I am looking at how I could modify this code such that fire was an independent action from movement.
I know I can easily add another separate output from the model so that the outputs would look something like this:
self.output = slim.fully_connected(rnn_out,a_size,
activation_fn=tf.nn.softmax,
weights_initializer=normalized_columns_initializer(0.01),
biases_initializer=None)
self.output2 = slim.fully_connected(rnn_out,1,
activation_fn=tf.nn.sigmoid,
weights_initializer=normalized_columns_initializer(0.01),
biases_initializer=None)
The thing I am struggling with is how then do I have to modify the value output and redefine the loss function. The value is still tied to the combination of the two outputs. Or is there a separate value output for each of the independent output. I feel like it should still only be one output as the value, but I am unsure how I them use that one value and modify the loss function to take this into account.
I was thinking of adding a separate term to the loss function so that the calculation would look something like this:
self.actions_1 = tf.placeholder(shape=[None],dtype=tf.int32)
self.actions_2 = tf.placeholder(shape=[None],dtype=tf.float32)
self.actions_onehot = tf.one_hot(self.actions_1,a_size,dtype=tf.float32)
self.target_v = tf.placeholder(shape=[None],dtype=tf.float32)
self.advantages = tf.placeholder(shape=[None],dtype=tf.float32)
self.responsible_outputs = tf.reduce_sum(self.output1 * self.actions_onehot, [1])
self.responsible_outputs_2 = tf.reduce_sum(self.output2 * self.actions_2, [1])
#Loss functions
self.value_loss = 0.5 * tf.reduce_sum(tf.square(self.target_v - tf.reshape(self.value,[-1])))
self.entropy = - tf.reduce_sum(self.policy * tf.log(self.policy))
self.policy_loss = -tf.reduce_sum(tf.log(self.responsible_outputs)*self.advantages) -
tf.reduce_sum(tf.log(self.responsible_outputs_2)*self.advantages)
self.loss = 0.5 * self.value_loss + self.policy_loss - self.entropy * 0.01
I am looking to know if I am on the right track here, or if there are resources or examples that I can expand off of.
First of all, the example you are mentioning don't need two output nodes. One output node with continuous output value is enough to solve. Also you should't use placeholder for advantage, but rather you should use for discounted reward.
self.discounted_reward = tf.placeholder(shape=[None],dtype=tf.float32)
self.advantages = self.discounted_reward - self.value
Also while calculating the policy loss you have to use tf.stop_gradient to prevent the value node gradient feedback contribution for policy learning.
self.policy_loss = -tf.reduce_sum(tf.log(self.responsible_outputs)*tf.stop_gradient(self.advantages))
I've been reading the docs to learn TensorFlow and have been struggling on when to use the following functions and their purpose.
tf.split()
tf.reshape()
tf.transpose()
My guess so far is that:
tf.split() is used because inputs must be a sequence.
tf.reshape() is used to make the shapes compatible (Incorrect shapes tends to be a common problem / mistake for me). I used numpy for this before. I'll probably stick to tf.reshape() now. I am not sure if there is a difference between the two.
tf.transpose() swaps the rows and columns from my understanding. If I don't use tf.transpose() my loss doesn't go down. If the parameter values are incorrect the loss doesn't go down. So the purpose of me using tf.transpose() is so that my loss goes down and my predictions become more accurate.
This bothers me tremendously because I'm using tf.transpose() because I have to and have no understanding why it's such an important factor. I'm assuming if it's not used correctly the inputs and labels can be in the wrong position. Making it impossible for the model to learn. If this is true how can I go about using tf.transpose() so that I am not so reliant on figuring out the parameter values via trial and error?
Question
Why do I need tf.transpose()?
What is the purpose of tf.transpose()?
Answer
Why do I need tf.transpose()? I can't imagine why you would need it unless you coded your solution from the beginning to require it. For example, suppose I have 120 student records with 50 stats per student and I want to use that to try and make a linear association with their chance of taking 3 classes. I'd state it like so
c = r x m
r = records, a matrix with a shape if [120x50]
m = the induction matrix. it has a shape of [50x3]
c = the chance of all students taking one of three courses, a matrix with a shape of [120x3]
Now if instead of making m [50x3], we goofed and made m [3x50], then we'd have to transpose it before multiplication.
What is the purpose of tf.transpose()?
Sometimes you just need to swap rows and columns, like above. Wikipedia has a fantastic page on it. The transpose function has some excellent properties for matrix math function, like associativeness and associativeness with the inverse function.
Summary
I don't think I've ever used tf.transpose in any CNN I've written.
I have some data in a pandas dataframe (although pandas is not the point of this question). As an experiment I made column ZR as column Z divided by column R. As a first step using scikit learn I wanted to see if I could predict ZR from the other columns (which should be possible as I just made it from R and Z). My steps have been.
columns=['R','T', 'V', 'X', 'Z']
for c in columns:
results[c] = preprocessing.scale(results[c])
results['ZR'] = preprocessing.scale(results['ZR'])
labels = results["ZR"].values
features = results[columns].values
#print labels
#print features
regr = linear_model.LinearRegression()
regr.fit(features, labels)
print(regr.coef_)
print np.mean((regr.predict(features)-labels)**2)
This gives
[ 0.36472515 -0.79579885 -0.16316067 0.67995378 0.59256197]
0.458552051342
The preprocessing seems wrong as it destroys the Z/R relationship I think. What's the right way to preprocess in this situation?
Is there some way to get near 100% accuracy? Linear regression is the wrong tool as the relationship is not-linear.
The five features are highly correlated in my data. Is non-negative least squares implemented in scikit learn ? ( I can see it mentioned in the mailing list but not the docs.) My aim would be to get as many coefficients set to zero as possible.
You should easily be able to get a decent fit using random forest regression, without any preprocessing, since it is a nonlinear method:
model = RandomForestRegressor(n_estimators=10, max_features=2)
model.fit(features, labels)
You can play with the parameters to get better performance.
The solutions is not as easy and can be very influenced by your data.
If your variables R and Z are bounded (for ex 0<R<1 -3<Z<2) then you should be able to get a good estimation of the output variable using neural network.
Using neural network you should be able to estimate your output even without preprocessing the data and using all the variables as input.
(Of course here you will have to solve a minimization problem).
Sklearn do not implement neural network so you should use pybrain or fann.
If you want to preprocess the data in order to make the minimization problem easier you can try to extract the right features from the predictor matrix.
I do not think there are a lot of tools for non linear features selection. I would try to estimate the important variables from you dataset using in this order :
1-lasso
2- sparse PCA
3- decision tree (you can actually use them for features selection ) but I would avoid this as much as possible
If this is a toy problem I would sugges you to move towards something of more standard.
You can find a lot of examples on google.