# Questions tagged [derivative]

For on-topic questions involving the mathematical concept of a derivative, i.e. $\frac{d}{dx} f(x)$. For purely mathematical questions about the derivative it is better to ask on math SE https://math.stackexchange.com/

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### Neural network learns to mimic distribution of classes in dataset instead of using signal from input

I'm trying to implement example from a classic AI paper named "Learning representations by back-propagating errors" by Hinton et al. Example aims at training network able to predict third ...
1 vote
23 views

### Why does the score test work for values longer in the tail that have a small log-likelihood derivative?

The score test says that we take the derivative of the log-likelihood at $H_0$ and divide it by the fisher information at $H_0$. $U(\theta )={\frac {\partial \log L(\theta \mid x)}{\partial \theta }}.$...
72 views

### Derivative-based effect size for Gaussian GAMs

It is often the realistic advice I have seen here that Gaussian GAMs are not regressions with which you can easily approximate an effect size for, as the effects are of course non-linear. However, we ...
10 views

1 vote
102 views

### First derivative of multivariate normal density with exchangeable correlation structure

As part of a proof, I need to take the first derivative of the log of the following multivariate normal density: $(2\pi)^{-k/2} |\Sigma|^{-1/2} \exp\left(\frac{-1}{2} x'\Sigma^{-1}x\right)$. In this ...
31 views

### Gradient vs differences to remove non-stationarity in time series?

When dealing with non-stationary time series (for instance, in auto-correlation analysis), differencing (computing absolute differences between consecutive samples/observations) is often regarded as ...
1 vote
20 views

### Elasticity estimates for zero-truncated negative binomial part in the hurdle model

I estimated a hurdle negative binomial regression model with zero-truncated negative binomial model as the count component in R using the pscl package. I wish to present elasticities for the count ...
23 views

### Useful value for rate of change

I want to create a simple representation of "rate of change" for a number of different metrics, which aren't really comparable between each-other. To illustrate my problem, let's say I have ...
1 vote
39 views

### Propagation of uncertainty in a derivative of a function [duplicate]

I've performed an ordinary least squares on a data set with one variable. For simplicity, let's say I've fitted a polynomial function $$f(x)=a+bx+cx^2+dx^3.$$ I obtain the best fit and the standard ...
151 views

### Probability Generating Function for The Difference of Two Binomially Distributed Random Variables?

Suppose I have 2 random variables: $X\sim \textrm{Bin}(m,p_1)$ and $Y\sim \textrm{Bin}(n,p_2).$ I want to find the distribution of $S=X-Y$ using the probability generating function ($PGF$) treating $S$...
35 views

### Trying to understand the derivation in the Information Bottleneck Method

I'm trying to understand the proofs on the The information bottleneck method paper by Tishby, Pereira and Bialek without luck. In particular, the second term in the functional derivative of the ...
1 vote
64 views

### Taking derivative of a function containing random variable wrt the variance of that variable [closed]

Say, I have a function containing a random variable such as $f(X)$, where $X$ is the random variable that comes from a family of random variables that differ only in the first and second moments (e....
118 views

### When are $f(X)$ and $f'(X)$ independent?

I want to know the effect of differentiation on the independence of random variables. For a random variable $X$, when are $f^{(n)}(X)$ and $f^{(n+k)}(X)$ independent?, $\forall n\geq0\;, k\geq 1$.
15 views

### Are some gradient weights equal?

I want to create a 3 layers neural network from scratch to perform linear regression. The first and the second layer have 2 neurons, and the last layer has one neuron. Feature vector x is divided into ...
73 views

### How to express backpropagation dE/dV using matrix

I'm new in NN and my math is not that good. I try to do manual calculation using NN model. I already know and try to calculate the feedforward and backward one by one using the formula. but when I try ...
1 vote
75 views

### The confusing derivation in the book 'Machine Learning: A Probabilistic Perspective' by Kevin P. Murphy

In the section 15.5 of the book 'Machine Learning: A Probabilistic Perspective' by Kevin P. Murphy, it discusses the Gaussian Process Latent Variable Model. The log-likelihood objective function is ...
48 views

### Derivative conditional moments binary random variable

Let $e$ be a continuously distributed RV with pdf $f$ and let $q( x )$ be a binary RV that depends on the former through the relation $q ( x ) = 1[h( x ) \geq e ]$, where $h$ is a well-behaved ...
1 vote
68 views

### What is the derivative of a set or a string? [closed]

Neural networks operate on numbers, and it's well-known what the derivative of numeric functions are, as well as what the derivative of matrix functions are. What about functions that operate on maps ...
126 views

### Is the Inverse Mills Ratio Strictly Decreasing?

As far as I know, the Inverse Mills ratio, $\lambda(x)=\phi(x)/\Phi(x)$, is decreasing in $x$. Thus, I am curious now whether $\lambda(x)$ is in fact strictly decreasing in $x$. To see this, I derived ...
76 views

1 vote
34 views

### I need to derivate the maximum likelihood of GLR function [closed]

I am trying to do the partial derivative of this function but I don't know how to include the $\theta$ inside my function to be able to apply the partial derivative in $\theta$. The likelihood ...