# All Questions

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### SVD of correlated matrix should be additive but doesn't appear to be

I'm just trying to replicate a claim made in the following paper, Finding Correlated Biclusters from Gene Expression Data, which is: Proposition 4. If $X_{IJ}=R_{I}C^{T}_{J}$. then we have: ...
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### Can the Mantel test be extended to asymmetric matrices?

The Mantel test is usually applied to symmetric distance/difference matrices. As far as I understand, an assumption of the test is that the measure used to define differences must be at least a ...
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### Help in how the paper derives the CRLB for Gaussian ARMA model

An univariate autoregressive process AR(p) process is expressed as $$y(n) = \sum_{j=1}^p a_jy(n-j) + u(n)$$ is excited by Gaussian sequence, $u$. Paper : On the Computation of the Cramer-Rao Bound ...
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### Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
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### Link between variance and pairwise distances within a variable

Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared Euclidean distances) ...
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### State-of-the-art in deduplication

What are the state-of-the-art methods in record deduplication? Deduplication is also sometimes called: record linkage, entity resolution, identity resolution, merge/purge. I know for example about ...
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### Model selection with Firth logistic regression

In a small data set ($n\sim100$ ) that I am working with, several variables give me perfect prediction/separation. I thus use Firth logistic regression to deal with the issue. If I select the best ...
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### Intraclass Correlation Coefficients (ICC) with Multiple Variables

Suppose I have measured some variable in siblings, which are nested within families. The data structure looks like this: family sibling value ------ ------- ----- 1 1 y_11 1 2 ...
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### Geometric understanding of PCA in the subject (dual) space

I am trying to get an intuitive understanding of how principal component analysis (PCA) works in subject (dual) space. Consider 2D dataset with two variables, $x_1$ and $x_2$, and $n$ data points ...
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### Speed, computational expenses of PCA, LASSO, elastic net

I am trying to compare computational complexity / estimation speed of three groups of methods for linear regression as distinguished in Hastie et al. "Elements of Statistical Learning" (2nd ed.), ...
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### Fitting the differences between two curves

The problem I'm trying to solve is to algorithmically figure out whether two curves converge or diverge in a graph (visually the problem is almost trivial). For examples: The left one is ...
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### Tail of the inverse cdf

I am almost sure I have already seen the following result in statistics but I can't remember where. If $X$ is a positive random variable and $E(X)<\infty$ then $\epsilon F^{-1}(1-\epsilon) \to 0$ ...
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### Are all models useless? Is any exact model possible — or useful?

This question has been festering in my mind for over a month. The February 2015 issue of Amstat News contains an article by Berkeley Professor Mark van der Laan that scolds people for using inexact ...
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### ANOVA: testing assumption of normality for many groups with few samples per group

Assume the following situation: we have a large number (e.g. 20) with small group sized (e.g. n = 3). I noticed that if I generate values from the uniform distribution, the residuals will look ...
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### Review paper on particle filter

I have found online a draft of an excellent review paper by Zhe Chen entitled "Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond". According to Google Scholar, the citation for ...
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### Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
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### Convolutional neural networks: Aren't the central neurons over-represented in the output?

[This question was also posed at stack overflow] The question in short I'm studying convolutional neural networks, and I believe that these networks do not treat every input neuron ...
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### Trouble finding good model fit for count data with mixed effects - ZINB or something else?

I have a very small data set on solitary bee abundance that I am having trouble analysing. It’s count data, and almost all the counts are in one treatment with most of the zeroes in the other ...
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### Comparing regression coefficients of same model across different data sets

I'm evaluating two (2) refrigerants (gases) that were used in the same refrigeration system. I have saturated suction temperature ($S$), condensing temperature ($D$), and amperage ($Y$) data for the ...
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### Example Of Strict von Neumann Inequality

Let $r(\pi, \delta)$ denote the Bayes risk of an estimator $\delta$ with respect to a prior $\pi$, let $\Pi$ denote the set of all priors on the parameter space $\Theta$, and let $\Delta$ denote the ...
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### Luce choice axiom, question about conditional probability

I'm reading Luce (1959). Then I found this statement: When a person chooses among alternatives, very often their responses appear to be governed by probabilities that are conditioned on the ...
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### Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio

I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows: Two URLs are compared for their ability to ...
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### Tail inequality on sum of product of normal variables

For independent random variables $x_1,..,x_n$ and $y_1,...,y_n$ following normal distribution $N(0,1)$, I need a simple estimate formula for $P(| \sum_1^n x_iy_i | \leq nt ) \leq e^{(?)}$ for ...