# Questions tagged [numerics]

Also known as Numerical Analysis, Numerics aims to provide methods and algorithms for numerical computations.

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### Algorithm for Irwin Hall Distribution [closed]

I've been trying to create a function for the Irwin Hall distribution that doesn't face the same issue as the unifed package implementation. Because the function suffers from numerical issues, I ...
250 views

### Training a physics informed neural network (PINN) in Julia using numerical gradient approximations

i am currently working on a small project which involves solving a pendulum differential equation $$a \ddot{x} + b \dot{x} + x = 0$$ The idea is to use a physics informed neural network which has two ...
67 views

### Numerical Stability when Inverse CDF Sampling from Truncated Density

Let $f(x)$ be the pdf of a random variable that we want to truncate to the interval $[a,b]$ and then sample from it. Let $F(x)$ denote the corresponding cdf. We can use inverse cdf sampling and ...
22 views

### Numerical Solution of two convoluted stable paretian random variables

I am trying to numerically compute the joint density of X and Y, where both are stable paretian distributed random variables with different alphas (1.4 and 1.7). I can compute the PDF via inversion ...
1 vote
57 views

### Can (or should) data dominated by two values be treated as categorical?

Problem. I have few data sets containing real values (aka observation and prediction). >85% of data values are oscillating between two values exactly (e.g. 0 or 10), while the rest are real numbers ...
61 views

### Understanding the Purpose of LogSumExp

According to Wikipedia, the LogSumExp function is a "smooth approximation to the maximum function mainly used by machine learning algorithms." Furthermore, The LSE function is often ...
1 vote
24 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 ...
32 views

### Numerically solving a sparse matrix equation

I want to find the $X$ that solves the matrix equation $$AX = B$$ with $A$ and $B$ known - $A$ and $X$ are rectangular, $A$ is $n \times m$ and $X$ is an $m \times n$, with $m > n$. (...
47 views

### Recreating equation in R returns different value

I am trying to understand an equation that is used to determine sample size. To do this, I am re-creating the example from a tutorial in R. However, when I re-create the example in R I get a different ...
65 views

### Establish numerical equivalence of statistical model across software

we are trying to establish numerical equivalence (within reasonable precision) for selected statistical models across programming languages such as SAS, R & Python or even different packages ...
1 vote
390 views

### Can I make Stata run lasso faster?

I am trying to run a lasso in Stata. I have 1.5 million observations and 1700 variables. Stata is running too slow. I am in 36th grid after 4 days. And get slower ever grid. I am using a 98GB Memory, ...
61 views

1k views

### log(1 - softmax(X))? [closed]

Let $\vec X$ be a vector. The $\vec V = \mathrm{logsoftmax}(\vec{X})$ function is defined as: $$v_i = \ln\left(\frac{e^{x_i}}{\sum_i e^{x_i}}\right)$$ This is provided in machine learning numerical ...
154 views

### Time series reference - Estimating ARIMA models using the Yule-Walker equations and Durbin-Levinson algorithm

I am doing some research related to time-series analysis, and hence was trying to find some good examples of implementations of the common estimation algorithms. For example, I wanted to fit some ...
128 views

### Reference request - time series analysis book with numerical algorithms

I am working on some applications of time series, and I wanted to find a book that has the numerical algorithms or pseudocode for computing things like AR models, and ARIMA models, using nonlinear ...
76 views

### Why is my QR decomposition updating code numerically off?

I apologize if this is the wrong place for this question; there are a number of potential points of failure each of which suggest either Math StackExchange or StackOverflow or here, but since the ...
834 views

75 views

1 vote