Questions tagged [computational-statistics]

Refers to the interface of statistics and computing; the use of algorithms and software for statistical purposes.

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164
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21answers
68k views

Does Julia have any hope of sticking in the statistical community?

I recently read a post from R-Bloggers, that linked to this blog post from John Myles White about a new language called Julia. Julia takes advantage of a just-in-time compiler that gives it wicked ...
77
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9answers
88k views

What algorithm should I use to detect anomalies on time-series?

Background I'm working in Network Operations Center, we monitor computer systems and their performance. One of the key metrics to monitor is a number of visitors\customers currently connected to our ...
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8answers
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Excel as a statistics workbench

It seems that lots of people (including me) like to do exploratory data analysis in Excel. Some limitations, such as the number of rows allowed in a spreadsheet, are a pain but in most cases don't ...
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6answers
30k views

What algorithm is used in linear regression?

I usually hear about "ordinary least squares". Is that the most widely used algorithm used for linear regression? Are there reasons to use a different one?
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4answers
70k views

How to sample from a normal distribution with known mean and variance using a conventional programming language?

I've never had a course in statistics, so I hope I'm asking in the right place here. Suppose I have only two data describing a normal distribution: the mean $\mu$ and variance $\sigma^2$. I want to ...
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14answers
2k views

If R were reprogrammed from scratch today, what changes would be most useful to the statistics community? [closed]

Many people in the statistics community and other academic fields use R as their primary language for data analysis and statistical computing. It is a wonderful ...
29
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5answers
2k views

What are examples of statistical experiments that allow the calculation of the golden ratio?

There are some very simple experiences that can be done by a kid at home, whose result allows one to statistically approach famous numbers such as $\pi$ or $e$. An example where $\pi$ shows up is ...
28
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12answers
21k views

Command-line tool to calculate basic statistics for stream of values [closed]

Is there any command-line tool that accepts the flow of numbers (in ascii format) from standard input and gives the basic descriptive statistics for this flow, such as min, max, average, median, RMS, ...
28
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7answers
11k views

Statistics concept to explain why you're less likely to flip the same number of heads as tails, as the number of flips increases?

I'm working on learning probability and statistics by reading a few books and writing some code, and while simulating coin flips I noticed something that struck me as slightly counter to one's naive ...
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2answers
13k views

How could stochastic gradient descent save time compared to standard gradient descent?

Standard Gradient Descent would compute gradient for the entire training dataset. ...
23
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4answers
12k views

C++ libraries for statistical computing

I've got a particular MCMC algorithm which I would like to port to C/C++. Much of the expensive computation is in C already via Cython, but I want to have the whole sampler written in a compiled ...
20
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3answers
916 views

Julia: Taking stock of how it has been doing

I came across a 2012 question that had a very good discussion about Julia as an alternative to R / Python for various types of Statistical Work. Here lies the original Question from 2012 about Julia'...
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4answers
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What kinds of statistical problems are likely to benefit from quantum computing?

We are at the advent of quantum computing, with quantum languages anticipating hardware quantum computers now available at high and low levels for simulated quantum computers. Quantum computing brings ...
18
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3answers
42k views

What is the difference between bagging and random forest if only one explanatory variable is used?

" The fundamental difference between bagging and random forest is that in Random forests, only a subset of features are selected at random out of the total and the best split feature from the subset ...
17
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6answers
9k views

Computation speed in R?

I have been tasked with moving one of our current large stochastic models out of SAS and into a new language. Personally, I prefer a traditional compiled language, but the PI wants me to check out R, ...
17
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2answers
3k views

How do ABC and MCMC differ in their applications?

To my understanding Approximate Bayesian Computation (ABC) and Markov Chain Monte Carlo (MCMC) have very similar aims. Below I describe my understanding of these methods and how I perceive the ...
17
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2answers
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How to fit a discrete distribution to count data?

I have the following histogram of count data. And I would like to fit a discrete distribution to it. I am not sure how I should go about this. Should I first superimpose a discrete distribution, say ...
16
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3answers
4k views

Do some of you use Google Docs spreadsheet to conduct and share your statistical work with others?

I know most of you probably feel that Google Docs is still a primitive tool. It is no Matlab or R and not even Excel. Yet, I am baffled at the power of this web based software that just uses the ...
16
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9answers
5k views

What books provide an overview of computational statistics as it applies to computer science?

As a software engineer, I'm interested in topics such as statistical algorithms, data mining, machine learning, Bayesian networks, classification algorithms, neural networks, Markov chains, Monte ...
16
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4answers
4k views

Who uses R with multicore, SNOW or CUDA package for resource intense computing?

Who of you in this forum uses ">R with the multicore, snow packages, or CUDA, so for advanced calculations that need more power than a workstation CPU? On which hardware do you compute these scripts? ...
16
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4answers
6k views

Updating linear regression efficiently when adding observations and/or predictors in R

I would be interested in finding ways in R for efficiently updating a linear model when an observation or a predictor is added. biglm has an updating capability when adding observations, but my data ...
15
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2answers
1k views

What are some important uses of random number generation in computational statistics?

How and why are random number generators (RNGs) important in computational statistics? I understand that randomness is important when choosing samples for many statistical tests to avoid bias towards ...
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4answers
11k views

Why is gradient descent required?

When we can differentiate the cost function and find parameters by solving equations obtained through partial differentiation with respect to every parameter and find out where the cost function is ...
13
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7answers
1k views

Making sense out of statistics theory and applications

I have recently graduated with my masters degree on medical and biological modeling, accompanied with engineering mathematics as a background. Even though my education program included a significant ...
13
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1answer
2k views

Closed form solution to lasso problem when data matrix is diagonal

$\newcommand{\diag}{\operatorname{diag}}$We have the problem: $$\min_{w\in\mathbb{R}^{d}}\left( \frac{1}{n}\sum_{i=1}^{n} \left( \langle w,x_{i}\rangle-y_{i} \right)^{2} +2\lambda||w||_1\right),$$ ...
12
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3answers
1k views

Using computer simulations to better understand statistical concepts at the graduate level

Hi I'm taking a graduate course in Statistics and we've been covering Test statistics, and other concepts. However, I am often able to apply the formulas and develop a sort-of intuition on how stuff ...
12
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1answer
327 views

Online, scalable statistical methods

This was inspired by Efficient online linear regression, which I found very interesting. Are there any texts or resources devoted to large-scale statistical computing, by which computing with ...
12
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1answer
1k views

How can I optimise computational efficiency when fitting a complex model to a large data set repeatedly?

I am having performance issues using the MCMCglmm package in R to run a mixed effects model. The code looks like this: ...
11
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1answer
675 views

Can someone explain like I am 5 year-old about this problem from Hastie's ESL Book?

I am working through Hastie's ESL book, and I am having a tough time with Question 2.3. The question is as follows: We are considering a nearest neighbor estimate at the origin, and the median ...
11
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4answers
1k views

Outlier Detection in Time-Series: How to reduce false positives?

I'm trying to automate outlier detection in time-series and I used a modification of the solution proposed by Rob Hyndman here. Say, I measure daily visits to a website from various countries. For ...
11
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1answer
7k views

What is this “maximum correlation coefficient”?

A typical image processing statistic is the use of Haralick texture features, which are 14. I am wondering about the 14th of these features: Given an adjacency map $P$ (which we can simply view an ...
11
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1answer
1k views

Finding a comparable Control group for a treatment group?

I have a treatment group of size 30 (30 schools in California) that used a math supplemental software. In a simple analysis, I'd like to compare students' average Math growth between our treatment ...
10
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3answers
17k views

Is it possible in R (or in general) to force regression coefficients to be a certain sign?

I'm working with some real world data and the regression models are yielding some counterintuitive results. Normally I trust the statistics but in reality some of these things can not be true. The ...
10
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2answers
458 views

How to sample from discrete distribution on the non-negative integers?

I have the following discrete distribution, where $\alpha,\beta$ are known constants: $$ p(x;\alpha,\beta) = \frac{\text{Beta}(\alpha+1, \beta+x)}{\text{Beta}(\alpha,\beta)} \;\;\;\;\text{for } x = 0,...
10
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4answers
299 views

Testing statistical software

What techniques/approaches are useful in testing statistical software? I'm particularly interested in programs that do parametric estimation using maximum likelihood. Comparing results to those from ...
10
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1answer
2k views

Efficient/fast Mahalanobis distance computation

Suppose I have $n$ data points $x_1,\dots,x_n$, each of which is $p$-dimensional. Let $\Sigma$ be the (non-singular) population covariance of these samples. With respect to $\Sigma$, what is the most ...
10
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2answers
2k views

Inverse covariance matrix vs covariance matrix in PCA

In PCA, does it make a difference if we pick principal components of the inverse covariance matrix OR if we drop eigenvectors of the covariance matrix corresponding to large eigenvalues? This is ...
10
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2answers
9k views

How to find optimal values for the tuning parameters in boosting trees ?

I realise that there are 3 tuning parameters in the boosting trees model, i.e. the number of trees (number of iterations) shrinkage parameter number of splits (size of each constituent trees) My ...
10
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3answers
15k views

Time Series Anomaly Detection with Python

I need to implement anomaly detection on several time-series datasets. I've never done this before and was hoping for some advice. I'm very comfortable with python, so I would prefer the solution be ...
10
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1answer
426 views

Fast computation/estimation of a low-rank linear system

Linear systems of equations are pervasive in computational statistics. One special system I have encountered (e.g., in factor analysis) is the system $$Ax=b$$ where $$A=D+ B \Omega B^T$$ Here $D$ is ...
9
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3answers
1k views

Mathematica's random number generator deviating from binomial probability?

So, let's say you flip a coin 10 times, and call that 1 "event". If you run, 1,000,000 of these "events", what is the proportion of events that have heads between 0.4 and 0.6? Binomial probability ...
9
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6answers
1k views

Books Similar to Introduction to Statistical learning

I'm looking for books similar to Introduction to Statistical Learning with Applications in R (ISLR), which is not too rigorous in terms of the mathematical treatment, but still able to provide you the ...
9
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1answer
10k views

How can I compute a posterior density estimate from a prior and likelihood?

I am trying to understand how to use Bayes' theorem to calculate a posterior but am getting stuck with the computational approach, e.g., in the following case it is not clear to me how to take the ...
9
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1answer
3k views

Is functional analysis and hilbert spaces useful in machine learning? If so, how?

I was wondering, how are hilbert spaces and functional analysis useful to machine learning? I thought machine learning was a mix of statistics, computer science and optimization. How does functional ...
9
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2answers
3k views

How to make R's gamm work faster?

Last night I started a complex calculation with gamm() and it took me... user system elapsed 9259.76 326.05 9622.64 (s) ......
9
votes
1answer
131 views

sampling cost of $O(d)$ versus $O(2^d)$

I came across the following simulation problem: given a set $\{\omega_1,\ldots,\omega_d\}$ of known real numbers, a distribution on $\{-1,1\}^d$ is defined by $$\mathbb{P}(X=(x_1,\ldots,x_d))\propto (...
9
votes
1answer
160 views

Algebraic classifiers, more information?

I have read Algebraic classifiers: a generic approach to fast cross-validation, online training, and parallel training and was amazed by the performance of the derived algorithms. However, it seems ...
8
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2answers
5k views

How to validate if a sample is independent and identically distributed

How can I check if the data is drawn i.i.d. from an unknown multivariate distribution?
8
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2answers
9k views

How to statistically compare two algorithms across three datasets in feature selection and classification?

Problem background: As part of my research, I have written two algorithms that can select a set of features from a data set (gene expression data from cancer patients). These features are then tested ...
8
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2answers
603 views

Bootstrap vs numerical integration

My understanding of the bootstrap approach is based on Wasserman's framework (almost verbatim): Let $T_n = g(X_1, ..., X_n)$ be a statistic ($X_i$ is the iid sample drawn from distribution $F$). ...

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