hearse
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Why bother with low rank approximations?
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17 votes

A low rank approximation $\hat{X}$ of $X$ can be decomposed into a matrix square root as $G=U_{r}\lambda_{r}^\frac{1}{2}$ where the eigen decomposition of $X$ is $U\lambda U^T$, thereby reducing the ...

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Similarity of two discrete fourier tranforms?
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12 votes

Spectral coherence, if used correctly would do it. Coherence is computed at each frequency-and hence is a vector. Hence, a sum of a weighted coherence would be a good measure. You would typically want ...

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Gibbs sampler from conditional distribution
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7 votes

There you go- Gibbs Sampler: The burning period is to reach some stationarity in the samples burning_period=5000 iterations=1000 y=matrix(nrow=(burning_period+iterations),ncol=3) a=matrix(nrow=...

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Are there methods to learn a projection method into euclidean space, given a set of pairwise distances?
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6 votes

Use Laplacian Eigenmaps, Locally Linear Embedding or Local Tangent Space Alignment. These methods map the distances in a low-dimensional space non-linearly, thereby preserving the local neighborhood/ ...

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How to correlate two time series, with possible time differences
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6 votes

Apply a lag operator on one time series, with the other fixed, and calculate the coherence of the cross-spectrum achieved against each lag. Find the lag that gives you the maximum coherence and ...

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Clear steps to calculate coherence between two time series
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4 votes

The following are the issues that I summarize succinctly in sequence, as each of them are an interesting problem in itself and then follow it up with my solutions: i) How to unlag two time-series so ...

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Why are eigen and svd decompositions of a covariance matrix based on sparse data yielding different results?
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4 votes

You need to do the sum of the absolute value of eigen values i.e, sum(abs(Eg$values)) and compare it with the sum of the singular values. They would be equal. The reason is that if you multiply the ...

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Dimensionality reduction on a huge binary matrix
4 votes

Nystrom Approximation based large scale SVD and Column sampling based SVD are used in this scenario. Check out sections 3.1, 3.2 and 3.3 in "Large-Scale Manifold Learning" by Ameet Talwalkar, Sanjiv ...

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What's the difference between principal component analysis and multidimensional scaling?
4 votes

Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a ...

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Why is k called representer of evaluation in the definition of kernel functions
3 votes

In an RKHS framework, any function $f(\cdot)$ can be minimized with a hilbert-norm minimizing solution, just by a linear combination of the kernels evaluated at the rest of the data points and $x$ ...

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p-value as a distance?
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3 votes

A specific case, where the p-values are generated from $\chi ^2$ tests over frequency tables were used as similarities and multidimensional scaling was applied in this paper: http://www.biomedcentral....

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Nonlinear principal component analysis MATLAB code
3 votes

See Matthias Scholz's site for the MATLAB code (the homepage includes references).

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How to distinguish between periodic and random impulse?
3 votes

The autocorrelation function(acf) of a random white noise signal will have an inpulse at zero, and the acf will be zero at other times meaning there is no periodicity or correlation at time lags. The ...

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R package for identifying relationships between variables
2 votes

You can use the DCOR function in the 'energy' package to compute a measure of non-linear dependency called distance correlation and plot as above. The issue with Pearson's correlation is that it can ...

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Best distance measure to use to compare vectors of angles
2 votes

This problem is called Distance Metric Learning. Every distance metric can be represented as $\sqrt{(x-y)^tA(x-y)}$ where $A$ is positive semi-definite. Methods under this sub-area, learn the optimal ...

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How does the test error pattern depend on the regularizer function?
2 votes

Yes-dependent on where the optimal cross-validated value of $\lambda$ lies-which is dependent on the true joint distribution that generates the features and the response (interpret as problem ...

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Response-distribution-dependent bias in random forest regression
2 votes

You should be estimating the optimal value of mtry and sampsize by minimizing the out of sample "cross-validated error" over a grid of different mtry, sampsize parameters, for any corresponding ...

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Is the absolute value of distance covariance a metric?
2 votes

Distance covariance and distance Correlation do not satisfy the triangular inequality. Pearson's correlation itself on centered data or otherwise, does not satisfy the inequality, and hence is known ...

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Cross correlation vs mutual information
2 votes

Cross correlation is used in time-frequency analysis and is a inner product with a lag-parameter obtained between two functions varying over time, where one function is evaluated at time $t$ and the ...

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Bias Correction for Estimator with known bias
1 votes

You may try the method of target estimation to reduce bias, if you have the expectation function estimated either computationally or through closed form expressions or closed form von-mises expansion ...

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Distributions on subsets of $\{1, 2, ..., J\}$?
1 votes

A sample from a k-determinantal point process models a distribution over subsets that encourages diversity, such that similar items are less likely to occur together in the sample. Refer to K-...

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Converting a list of partial rankings into a global ranking
1 votes

Plackett-Luce ranking models deal with this problem and are a likelihood based technique where the likelihood is maximized using a majorization-maximization routine, which is similar to Expectation ...

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Why is this regret a good choice for a multi-armed bandit?
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1 votes

I have understood this far- recently-looking for the difference between $\mathbb{E}[ \max_j \sum_{j=1}^T x_j(t) - G_A(T) ]$ and $\max_j \mathbb{E}[ \sum_{j=1}^T x_j(t) - G_A(T) ]$ obviously, the ...

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PCA, ICA and Laplacian eigenmaps
1 votes

Unlike PCA- Laplacian eigenmaps uses the generalized eigen vectors corresponding to the smallest eigenvalues. It skips the eigen vector with the smallest eigen value (could be zero), and uses the ...

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Method to classify and recode high and low probability regions?
1 votes

This is exactly the focus of active learning. Do watch this video by Sanjoy Dasgupta, John Langford: http://videolectures.net/icml09_dasgupta_langford_actl/ to understand the framework. In a way, it ...

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Given a set of sub-graphs, how to infer the underlying graph?
1 votes

"Exponential Random Graph Models" - precisely deal with the first case in your question.

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To use Discrete Fourier Transform to invert a covariance matrix
1 votes

Have you tried a correction- by adding a small $\epsilon$ perturbation to the diagonal of the matrix you are trying to invert. This is a standard processing routine used to defer the singularity issue ...

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Hypothesis test for correlation between Gamma random variables
0 votes

You can use distance correlation by Szekely. R Package is called 'energy'. It is distribution agnostic and gamma doesn't matter. You can get a p-value of the test as well.

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Good algorithm for processing positional estimates
0 votes

Data Depth is a robust measure of central tendency and is interpretable. Tukey's data depth, Liu's simplicial depth are some examples of data depth. The following is an R package that has functions to ...

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