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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Information coefficient as loss function of XGBoost

I am trying to train an XGBoost regressor for stock price prediction. I want to customize the objective function to be Information Coefficient (IC). The definition of IC is the Pearson correlation ...
1 vote
27 views

How can I prove monotonicity of slope MLE in EIV regression model?

I'm trying to figure out Casella and Berger Exercise 12.4(c), regarding monotonicity of the maximum likelihood estimator of the slope of an errors-in-variables regression model. The goal is to show ...
• 11
43 views

Derivative of the multivariate normal cumulative distribution function (CDF) with reparameterisation [duplicate]

I would like to learn how to calculate the derivatives of a multivariate normal cumulative distribution function (MVN CDF) w.r.t. certain elements by using the derivatives of the same MVN CDF w.r.t. ...
• 31
23 views

How to determine statistical significance for a time series and forecasts?

With a simple example of mortality rates, and a basic three-year mean baseline: ...
10 views

129 views

derivatives and distribution of a 3-dimensional copula in R

I am looking for a way to calculate in the R software, the distribution, the density and the derivatives (of order 1, 2) partial of a Gaussian copula of dimension 3. Indeed, I have three variables (u1,...
154 views

How did we derive the least square estimator using OLS?

How does multiplying a matrix with its transpose equal "minimizing" it? When calculating the partial derivative, where does the X' come from? Why setting the value of third equation to 0 is ...
372 views

Derivative error with respect to bias in binary cross entropy

I will do research using NN with 1 hidden layer. To calculate loss using binary cross entropy and for the activation function using sigmoid. I found the derivative formula from Sadowski, 2016 (link: ...
• 47
147 views

Given a softmax output layer, what does it mean to "follow the gradient"? Usually that would consist in "increasing the output" but obviously the softmax has no notion of "...
• 1,217
119 views

four-point forward-difference formula using Newton's form for first order derivative [closed]

We know that ${f'(x) \approx \frac{f(x+h)- f(x)}{h}}$. If we have three points ${x_0 = x-h}$, ${x_1 = x}$, ${x_2 = x + h}$, we can compute the 3-point centered-difference formula using the Newton's ...
• 217
27 views

Derivative of multivariate normal cdf with respect to it’s arguments [duplicate]

I'm using a result from the dissertation of Poddar(2016, link) and he states the following in his appendix A1: We will use the well known property, stated here for completeness, of the multivariate ...
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1 vote
73 views

I am reading this article, which explains how the algorithm replaces the actual loss function with so-called 2nd order Taylor expansion. I can understand til Step 4, and can't understand step 5. I ...
• 109
1 vote
27 views

A question on computational complexity of a numerical differentiation (equation (5.77)) in Bishop's Pattern Recognition and Machine Learning

In page 249 of Christopher M. Bishop's book "Pattern Recognition and Machine Learning", it is said Again, the implementation of such algorithms can be checked by using numerical ...
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The book "Pattern Recognition and Machine Learning" by Christopher M. Bishop says in page 248 ... for softmax outputs we have: \frac{\partial y_k}{\partial a_l}=\delta_{kl}y_k-y_ky_l.\tag{...