I measured the spectrum of an X-ray tube with a Geiger counter. Such data aren't normally distributed, but instead they follow the Poisson distribution. I want to fit a curve to the measured data:
a = 1
b = 1
f(x) = a*(x/b - 1)/x**2
fit f(x) 'data.txt' via a,b
This will, however, perform the least-squares regression, which is theoretically wrong in this case. Instead I need to perform the Poisson regression. How do I achieve this?
The link function of the Poisson distribution is ln(μ). Is there a way to use this information, eg. with the gnuplot's link command?
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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 have been following cs231n lectures of Stanford and trying to complete assignments on my own and sharing these solutions both on github and my blog. But i'm having a hard time on understanding how to modelize backpropagation. I mean i can code modular forward and backward passes but what bothers me is that if i have the model below : Two Layered Neural Network
Lets assume that our loss function here is a softmax loss function. In my modular softmax_loss() function i am calculating loss and gradient with respect to scores (dSoft = dL/dY). After that, when i'am following backwards lets say for b2, db2 would be equal to dSoft*1 or dW2 would be equal to dSoft*dX2(outputs of relu gate). What's the chain rule here ? Why isnt dSoft equal to 1 ? Because dL/dL would be 1 ?
The softmax function is outputs a number given an input x.
What dSoft means is that you're computing the derivative of the function softmax(x) with respect to the input x. Then to calculate the derivative with respect to W of the last layer you use the chain rule i.e. dL/dW = dsoftmax/dx * dx/dW. Note that x = W*x_prev + b where x_prev is the input to the last node. Therefore dx/dW is just x and dx/db is just 1, which means that dL/dW or simply dW is dsoftmax/dx * x_prev and dL/db or simply db is dsoftmax/dx * 1. Note that here dsoftmax/dx is dSoft we defined earlier.
I am trying to fit the model from Frome(1983) in R using poisson Regression, but i dont know how add the exposure: ln(person-years), the model is:
ln E(Y|X)= ln(person-years)+ B0+ B1X1+ B2X2.
Do you know how fit that ?
You can perform poisson regression analysis using the below R code.
m1<- glm(y ~ offset(log(person-years))+X1+X2, family="poisson", data=dat)
summary(m1)
Because you use an offset of 'log(person-years)', the coefficient of 'log(person-years)' is forced to be 1.
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).
So, I have a vector that corresponds to a given feature (same dimensionality). Is there a package in Julia that would provide a mathematical function that fits these data points, in relation to the original feature? In other words, I have x and y (both vectors) and need to find a decent mapping between the two, even if it's a highly complex one. The output of this process should be a symbolic formula that connects x and y, e.g. (:x)^3 + log(:x) - 4.2454. It's fine if it's just a polynomial approximation.
I imagine this is a walk in the park if you employ Genetic Programming, but I'd rather opt for a simpler (and faster) approach, if it's available. Thanks
Turns out the Polynomials.jl package includes the function polyfit which does Lagrange interpolation. A usage example would go:
using Polynomials # install with Pkg.add("Polynomials")
x = [1,2,3] # demo x
y = [10,12,4] # demo y
polyfit(x,y)
The last line returns:
Poly(-2.0 + 17.0x - 5.0x^2)`
which evaluates to the correct values.
The polyfit function accepts a maximal degree for the output polynomial, but defaults to using the length of the input vectors x and y minus 1. This is the same degree as the polynomial from the Lagrange formula, and since polynomials of such degree agree on the inputs only if they are identical (this is a basic theorem) - it can be certain this is the same Lagrange polynomial and in fact the only one of such a degree to have this property.
Thanks to the developers of Polynomial.jl for leaving me just to google my way to an Answer.
Take a look to MARS regression. Multi adaptive regression splines.