"References" is our generic tag for questions seeking information about books, papers, presentations, videos of lectures, on-line tutorials, etc., regarding any subject matter that is on-topic for Cross Validated.

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Resources for Determining Value-Added by Parameter Sweeps

I am working on a project that aims to use Design of Experiments to improve our testing process. We are performing tests using a parameter sweeps of numerous input variables (40+). Each input variable ...
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2answers
56 views

Meaning of (and proof of) “RNN can approximate any algorithm”

Recently I read that a recurrent neural network can approximate any algorithm. So my question is: what does this exactly mean and can you give me a reference where this is proved?
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1answer
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Variance of the modulus of a random variable

Let $X$ be a random variable with mean $\mu$ and variance $\sigma^2$. What is the upper-bound on the variance of $Y=\left|X\right|$? My gut feeling says that $\operatorname{Var}(Y) \leq \operatorname{...
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Unable to recreate the sine function in Figure 5.3 - Pattern recognition and machine learning (Bishop)

I'm trying to recreate the sine function according to Figure 5.3. Of course since in the range [-1;1] this function won't look like the one in the figure (because the closest minima and maxima are x = ...
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Pattern recognition and machine learning (Bishop) - Figure 5.3: Something is wrong with the sine function

In Figure 5.3, Pattern recognition and machine learning (Bishop), the author says he fitted 4 function: f(x) = x^2; f(x) = sin(x) ; f(x) = abs(x); f(x) = Heaviside(x), using 50 points chosen uniformly ...
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1answer
87 views

What are multi-variable calculus pre-requisite for Machine Learning

I wanted to complete calculus pre-requisites for machine learning class. I am doing an online course of multi-variable calculus. Can someone please suggest what lectures after Lecture 15 are relevant. ...
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1answer
32 views

Pattern recognition and machine learning (Bishop) - Derivation of Evidence approximation

I'm reading section 3.5 of the PRML book, entitled Evidence approximation, and is having difficulty understanding this part: . I don't understand how to derive (3.75) from (3.74). The author says it ...
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Citation of a particular paper discussing the phrase “representative” sample

Some time ago (like decades?) I read a paper that gently explained why the phrase "representative sample" is an unfortunate and misleading usage, and why one should speak of random samples, perhaps in ...
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Reference request about feature maps in ML

Can someone kindly link to some recent papers on understanding feature maps in ML? It would help to get an idea of what are the recent issues there that people have been working on with regards to ...
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7answers
2k views

What are some examples of anachronistic practices in statistics?

I am referring to practices that still maintain their presence, even though the problems (usually computational) they were designed to cope with have been mostly solved. For example, Yates' ...
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1answer
40 views

Good text on nonlinear regression (M.S. graduate-level)?

I've covered a linear models sequence where the classes discussed linear models using matrices, covering various experimental designs (split-plot, for example), ANOVA using matrices, and ending with ...
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How much variance is captured by the RFF maps?

The RFF maps here are possibly the most used feature maps. I was wondering if there are cases where anyone has theoretically estimated the total variance captured by these maps? Is any simplification ...
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2answers
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Seeking a Recommendation on Machine Learning Books for Biological Research

I am an undergraduate student studying mathematics and microbiology. I recently got a research project to study the evolution of viruses from the computational perspective, particularly from machine ...
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0answers
23 views

Normalized term frequency comparisons across documents of differing length & language

I aim to infer on the prevalence of terms across and within corpora of different languages (where document length varies within and across corpora). Given Zipf’s and Heap’s laws a simple tf/n seems ...
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2answers
65 views

Good examples/books/resources to learn about applied machine learning (not just ML itself)

I've taken an ML course previously, but now that I am working with ML related projects at my job, I am struggling quite a bit to actually apply it. I'm sure the stuff I'm doing has been researched/...
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1answer
33 views

Book about time series analysis in Stata

Does somebody know a good book which outlines the time series analysis in Stata, that is, the various commands explained. I am aware of the Stata manuals; however, they are not that user friendly for ...
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1answer
22 views

Reference for incremental sandwich covariance from biglm?

I am working on some similar methods to Lumley's biglm wrapper around Miller's AS274 algorithm, and I can't seem to find a reference for his incremental Huber/White ...
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13 views

Literature (guidelines) on unbalancedness in two-way within-subject ANOVA

I am looking for literature (guidelines) which discuss the consequences of unbalanced designs on running a (two-way) within-subject ANOVA and pros/cons of various counter-measures. I came up with ...
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1answer
33 views

Reference Books on Asymptotic theory of Statistics and Probability

Can anyone suggest me some good reference books on Asymptotic Theory of Statistics and Probability for students pursuing a post-graduate degree in Statistics ? It would be very much helpful if the ...
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4answers
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Which book should I read to get started with machine learning, Elements of statistical learning or Pattern recognition in machine learning?

I want to learn machine learning. I found tons of material on the internet but couldn't decide which book to get started with.
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1answer
78 views

Logistic Regression Problem

The following table gives data on income in thousand dollars (x), the number of families (N) at income x and the number of families owning a house (n). ...
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0answers
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What does “complete i” subscript mean in Gelman's model of incumbency in congressional elections?

I'm having a look at section 14.3, "Regression for causal inference: incumbency in congressional elections" in Gelman et al's Bayesian Data Analysis, third edition, pages 358-362. I'm looking for the ...
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0answers
13 views

Posterior pointwise uncertainty of multivariate normal-Wishart (variational GMM)

Given a variational mixture of Gaussians (as per, e.g., Chapter 10 of Bishop, 2006), we can compute the posterior predictive pdf: $$ \left\langle p(x|\alpha,\beta,\nu,\mu,V) \right\rangle $$ where $\...
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0answers
9 views

Reference for forecasting nonstationary variables

My goal is to extrapolate / forecast data up to 10, 20, 100 years depending on certain independent variables. Is there like a publication or a book that I could follow that specifically pertains to ...
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1answer
53 views

Intraclass correlation coefficient in Bayesian statistics

I need some references about intraclass correlation coefficient in Bayesian statistics and hypothesis testing. I already take a look in A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian ...
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Bayesian inference via approximate data likelihood

Suppose that we have a very large i.i.d. sample $x_1,...,x_n$ and a data likelihood defined by $$p(x | \theta,\beta) = \prod_ip(x_i | \theta,\beta)$$. Further suppose that $\theta$ is the parameter ...
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Validating regression - common and best practice

Is there a reference setting out a best practice way to validate a regression (such as Lasso, but in general any automated regression), and what is done in practice? My motivation for the question is ...
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0answers
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Factor Analysis with low sample size

Does anyone know of references to support conducting EFA with a low sample size?
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1answer
27 views

convergence of geometric mean/harmonic mean

Does any one know papers regarding the convergence of geometric mean or harmonic mean in probability, parallel to central limit theorem?
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10 views

“*usefulness*” is a bivariate property used in Regression and Anova. Has a generalization (trivariate) analogon been discussed?

Just for selfstudy/exercising of algorithms I looked at the computation of the "usefulness"-measure in multiple regression, which means the part of variance which one independent item contributes to ...
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1answer
81 views

Learning functional analysis for studying kernels

I'm trying to learn more about kernel machine theory and I've discovered that I need to learn a lot of background math, and so I'm looking for some good resources for this. In particular: I've got ...
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1answer
50 views

Text to read to prepare for course in advanced data analysis (second-level data analysis graduate course)

I have some free time this summer and would like to read something to prepare for the "Advanced Data Analysis" course I will be taking. This second level course, according to the course catalog, ...
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1answer
43 views

References for learning about online random forests

I am new to concepts of random forest. Can someone provide relevant sites where I could get learn more about using random forests to learn incoming data like an online algorithm?
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Treatment changing over time

I have a problem with the identification technique of my research paper. I would like to estimate the causal effect of a policy (the introduction of a budget balance rule) on the composition of ...
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1answer
18 views

References on ARDL model

Please suggest books/references on ARDL model and ARDL bounds test approach to study.
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28 views

How to predict link using rooted pagerank

I am studying link prediction in social networks and I am trying to implement algorithms like common neighbors. I can't understand rooted Pagerank; it's an algorithm who calculate the similarity ...
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Reference summarizing various machine learning algorithms' computational complexity

For example, suppose you train a linear regression model using the Normal Equation, on a training set $\mathbf{X}$ containing $m$ instances and $n$ features. The Normal Equation requires computing $(\...
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7 views

General strategy of confounding design

Example: Suggest a confouding scheme for a $2^8$ experiment in 16 blocks of 16, assuming that all 2-factor and 3-factor interactions are to be estimated. Please find the confounding design. Question: ...
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0answers
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Where did sublinear tf-idf originate?

I have often come across this weighting scheme for tf-idf (term frequency - inverse document frequency) in text mining. I am wondering where it came from (for citations). I've searched very rigorously,...
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0answers
9 views

Counting repetitions

I would like to count how many times a pattern occurs in a signal and I'm confused what is the best method to do that. As I see it I could train a classifier to recognize the pattern that I'm ...
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0answers
11 views

Presenting finite sample examination of asymptotics

From statistical theory, we often obtain results such as $\sqrt n (\theta - \hat \theta) \rightarrow_d N(0, \sigma)$ ie we have a normal limiting distribution. Because this formula says nothing ...
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Reference Request: Kernel density estimation for classification problems

I'm looking for resources dealing with problems like in this question: We have data with a continuous independent variable $X$ and a discrete dependent variable $Y$ (with values $y_1, y_2$). How (and ...
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23 views

Multivariate Linear Regression with Linear Constraints

Consider random samples $z_1,\ldots, z_N\in \mathbb{R}^n$ distributed according to $z_i\sim\mathcal{N}(T\cdot q_i, \Sigma)$ with $T,\Sigma\in\mathbb{R}^{n\times n}$ and $q_i\in\mathbb{R}^n$. If the $...
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Where can I find ressouce for big multi valued time series? [closed]

for my job I need to find timeseries datas to fit our algorithms. I have encoutered many links for Keogh archive and his work in general, but provided datas are "too clean" i.e datas are aligned, ...
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1answer
52 views

AIC, model selection and overfitting

I am looking for references that specifically show that Akaike's Information Criterion (AIC), or its corrected form (AICc), can in some practical applications -- that is, not in the asymptotic regime -...
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1answer
130 views

do(x) operator meaning?

I have seen the $do(x)$ operator everywhere in some literature review I am doing on Causality (see, for instance this wikipedia entry). However, I cannot find a formal and general definition of this ...
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0answers
14 views

Unbiased proportion estimate for a 2-component Gaussian mixture model?

Suppose I have a 2-component Gaussian mixture model of dimension $p$, where each mixture has the same covariance matrix: $$ \pi_1 \mathcal{N}(\mu_1, \Sigma) + \pi_0 \mathcal{N}(\mu_0, \Sigma) $$ ...
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1answer
16 views

Deviation due to conditioning

Let $A$ and $B$ be random variables. Can we upper-bound the following expression? $$ \mathbb{E}\Big[\Big(\mathbb{E}[A|B] - \mathbb{E}[A]\Big)^2\Big] $$ The above looks classical research. However, I ...
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Estimating cross-spectrum of random fields

There is a cross-periodogram (and it's smoothed versions) for estimating cross-spectral density of stationary bivariate process ($\xi_t = (X_t,Y_t), t\in \mathbf R) $. Is there a cross-periodogram for ...
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1answer
27 views

weak classifier with weak features

I have a set of weak features, and I am looking to create classifier based on them (it will only be weak given the noisy data). I am only trying to be right in ~60% of the case (that's enough for my ...