I would like to make a prediction by using Least Squares Support Vector Machine for Regression, which is proposed by Suykens et al. I am using LS-SVMlab, which you can find the MATLAB toolbox here. Let's consider I have an independent variable X and a dependent variable Y, that both are simulated. I am following the instructions in the tutorial.
>>X = linspace(-1,1,50)’;
>>Y = (15*(X.^2-1).^2.*X.^4).*exp(-X)+normrnd(0,0.1,length(X),1);
>>type = ’function estimation’;
>>[gam,sig2] = tunelssvm({X,Y,type,[], [],’RBF_kernel’},’simplex’,...’leaveoneoutlssvm’,’mse’});
>>[alpha,b] = trainlssvm({X,Y,type,gam,sig2,’RBF_kernel’});
>>plotlssvm({X,Y,type,gam,sig2,’RBF_kernel’},{alpha,b});
The code above finds the best parameters using simplex method and leave-one-out cross validation and trains the model and give me alphas (support vector values for all the data points in the training set) and b coefficients. However, it does not give me the predictions of the variable Y. It only draws the plot. In some articles, I saw plots like the one below,
As I said before, the LS-SVM toolbox does not give me the predicted values of Y, it only draws the plot but no values in the workspace. How can I get these values and draw a graph of predicted values together with actual values?
There is one solution that I think of. By using X values in the training set, I re-run the model and get the prediction of values Y by using simlssvm command but it does not seem reasonable to me. Any solution that you can offer? Thanks in advance.
I am afraid you have answered your own question. The only way to obtain the prediction for the training points in LS-SVMLab is by simulating the training points after training your model.
[yp,alpha,b,gam,sig2,model] = lssvm(x,y,'f')
when u use this function yp is the predicted value
Related
if the inputs to my model are x,y,z and my outputs are continuous variables a,b,c,d I can obviously use the model to predict the vector [a,b,c,d] from [x,y,z].
However what happens if I find myself in a situation whereby I have say value b as a prior, before inference? Can i run the network in a manner such that I am predicting [a,c,d] based on [x,y,z,b]?
Real World example: I have an image with pixel locations (x,y) and pixel values (R,G,B). I then build a neural implicit model to predict pixel values based on pixel locations, say now I have a situation where I have the green values for some pixels as well as their locations, can I use these green values as a prior with my original network to get an improved result. Note that I am not interested in training a new network on said data.
In mathematical terms: I have network f(x,y,z) -> (a,b,c,d) how can I perform f(x,y,z|b) -> (a,c,d)?
I have not tried much here, thinking of maybe passing the prior value back through the network but am kinda lost.
I am beginner in deep learning.
I am using this dataset and I want my network to detect keypoints of a hand.
How can I make my output layer's nodes to be in range [-1, 1] (range of normalized 2D points)?
Another problem is when I train for more than 1 epoch the loss gets negative values
criterion: torch.nn.MultiLabelSoftMarginLoss() and optimizer: torch.optim.SGD()
Here u can find my repo
net = nnModel.Net()
net = net.to(device)
criterion = nn.MultiLabelSoftMarginLoss()
optimizer = optim.SGD(net.parameters(), lr=learning_rate)
lr_scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer=optimizer, gamma=decay_rate)
You can use the Tanh activation function, since the image of the function lies in [-1, 1].
The problem of predicting key-points in an image is more of a regression problem than a classification problem (especially if you're making your model outputs + targets fall within a continuous interval). Therefore, I suggest you use the L2 Loss.
In fact, it could be a good exercise for you to determine which loss function that is appropriate for regression problems provides the lowest expected generalization error using cross-validation. There's several such functions available in PyTorch.
One way I can think of is to use torch.nn.Sigmoid which produces outputs in [0,1] range and scale outputs to [-1,1] using 2*x-1 transformation.
I am getting started with deep learning and have a basic question on CNN's.
I understand how gradients are adjusted using backpropagation according to a loss function.
But I thought the values of the convolving filter matrices (in CNN's) needs to be determined by us.
I'm using Keras and this is how (from a tutorial) the convolution layer was defined:
classifier = Sequential()
classifier.add(Conv2D(32, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))
There are 32 filter matrices with dimensions 3x3 is used.
But, how are the values for these 32x3x3 matrices are determined?
It's not the gradients that are adjusted, the gradient calculated with the backpropagation algorithm is just the group of partial derivatives with respect to each weight in the network, and these components are in turn used to adjust the network weights in order to minimize the loss.
Take a look at this introductive guide.
The weights in the convolution layer in your example will be initialized to random values (according to a specific method), and then tweaked during training, using the gradient at each iteration to adjust each individual weight. Same goes for weights in a fully connected layer, or any other layer with weights.
EDIT: I'm adding some more details about the answer above.
Let's say you have a neural network with a single layer, which has some weights W. Now, during the forward pass, you calculate your output yHat for your network, compare it with your expected output y for your training samples, and compute some cost C (for example, using the quadratic cost function).
Now, you're interested in making the network more accurate, ie. you'd like to minimize C as much as possible. Imagine you want to find the minimum value for simple function like f(x)=x^2. You can start at some random point (as you did with your network), then compute the slope of the function at that point (ie, the derivative) and move down that direction, until you reach a minimum value (a local minimum at least).
With a neural network it's the same idea, with the difference that your inputs are fixed (the training samples), and you can see your cost function C as having n variables, where n is the number of weights in your network. To minimize C, you need the slope of the cost function C in each direction (ie. with respect to each variable, each weight w), and that vector of partial derivatives is the gradient.
Once you have the gradient, the part where you "move a bit following the slope" is the weights update part, where you update each network weight according to its partial derivative (in general, you subtract some learning rate multiplied by the partial derivative with respect to that weight).
A trained network is just a network whose weights have been adjusted over many iterations in such a way that the value of the cost function C over the training dataset is as small as possible.
This is the same for a convolutional layer too: you first initialize the weights at random (ie. you place yourself on a random position on the plot for the cost function C), then compute the gradients, then "move downhill", ie. you adjust each weight following the gradient in order to minimize C.
The only difference between a fully connected layer and a convolutional layer is how they calculate their outputs, and how the gradient is in turn computed, but the part where you update each weight with the gradient is the same for every weight in the network.
So, to answer your question, those filters in the convolutional kernels are initially random and are later adjusted with the backpropagation algorithm, as described above.
Hope this helps!
Sergio0694 states ,"The weights in the convolution layer in your example will be initialized to random values". So if they are random and say I want 10 filters. Every execution algorithm could find different filter. Also say I have Mnist data set. Numbers are formed of edges and curves. Is it guaranteed that there will be a edge filter or curve filter in 10?
I mean is first 10 filters most meaningful most distinctive filters we can find.
best
I have a good (or at least a self-consistent) calibration set and have applied PCA and recently PLS regression on n.i.r. spectrum of known mixtures of water and additive to predict the percentage of additive by volume. I thus far have done self-calibration and now want to predict the concentration from the n.i.r.spectrum blindly. Octave returns XLOADINGS, YLOADINGS, XSCORES, YSCORES, COEFFICIENTS, and FITTED with the plsregress command. The "fitted" is the estimate of concentration. Octave uses the SIMPLS approach.
How do I use these returned variables to predict concentration give a new samples spectrum?
Scores are usually denoted by T and loadings by P and X=TP'+E where E is the residual. I am stuck.
Note that T and P are X scores and loadings, respectively. Unlike PCA, PLS has scores and loadings for Y as well (usually denoted U and Q).
While the documentation of plsregress is sketchy at best, the paper it refers to Sijmen de Jong: SIMPLS: an alternativ approach to partial least squares regression Chemom Intell Lab Syst, 1993, 18, 251-263, DOI: 10.1016/0169-7439(93)85002-X
discusses prediction with equations (36) and (37), which give:
Yhat0 = X0 B
Note that this uses centered data X0 to predict centered y-values. B are the COEFFICIENTS.
I recommend that as a first step you predict your training spectra and make sure you get the correct results (FITTED).
I was asked to create a leg follower robot (I already did it) and in the second part of this assignment I have to develop a Kalman filter in order to improve the following process of the robot. The robot gets from the person the distance where she is to the robot and also the angle (it is a relative angle, because the reference is the robot itself, not absolute x-y coordinates)
About this assignment I have a serious doubt. Everything I have read, every sample I have seen about kalman filter has been in one dimension (a car running distance or a rock falling from a building) and according to the task I would have to apply it in 2 dimensions. Is it possible to apply a kalman filter like this?
If it is possible to calculate kalman filter in 2 dimensions then I would understand that what is asked to do is to follow the legs in a linnearized way, despite a person walks weirdly (with random movements) --> About this I have the doubt of how to establish the function of the state matrix, could anyone please tell me how to do it or to tell me where I can find more information about this?
thanks.
Well you should read up on Kalman Filter. Basically what it does is estimate a state through its mean and variance separately. The state can be whatever you want. You can have local coordinates in your state but also global coordinates.
Note that the latter will certainly result in nonlinear system dynamics, in which case you could use the Extended Kalman Filter, or to be more correct the continuous-discrete Kalman Filter, where you treat the system dynamics in a continuous manner and the measurements in discrete time.
Example with global coordinates:
Assuming you have a small cubic mass which can drive forward with velocity v. You could simply model the dynamics in local coordinates only, where your state s would be s = [v], which is a linear model.
But, you could also incorporate the global coordinates x and y, assuming we are moving on a plane only. Then you would have s = [x, y, phi, v]'. We need phi to keep track of the current orientation since the cube can only move forward in respect to its orientation of course. Let's define phi as the angle between the cube's forward direction and the x-axis. Or in other words: With phi=0 the cube would move along the x-axis, with phi=90° it would move along the y-axis.
The nonlinear system dynamics with global coordinates can then be written as
s_dot = [x_dot, y_dot, phi_dot, v_dot]'
with
x_dot = cos(phi) * v
y_dot = sin(phi) * v
phi_dot = ...
v_dot = ... (Newton's Law)
In EKF (Extended Kalman Filter) Prediction step you would use the (discretized) equations above to predict the mean of the state in the first step of and the linearized (and discretized) equations for prediction of the Variance.
There are two things to keep in mind when you decide what your state vector s should look like:
You might be tempted to use my linear example s = [v] and then integrate the velocity outside of the Kalman Filter in order to obtain the global coordinate estimates. This would work, but you would lose the awesomeness of the Kalman Filter since you would only integrate the mean of the state, not its variance. In other words, you would have no idea what the current uncertainties for your global coordinates are.
The second step of the Kalman Filter, the measurement or correction update, requires that you can describe your sensor output as a function of your states. So you may have to add states to your representation just so that you can express your measurements correctly as z[k] = h(s[k], w[k]) where z are measurements and w is a noise vector with Gaussian distribution.