Questions tagged [high-dimensional]
Pertains to a large number of features or dimensions (variables) for data. (For a large number of data points, use the tag [large-data]; if the issue is a larger number of variables than data, use the [underdetermined] tag.)
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Bound of operator norm for Gaussian ensemble (wainwright example 6.2)
Consider $W \in \mathbb{R}^{n \times d}$ generated with i.i.d. $N(0,1)$ entries, theorem 6.1 in the Martin Wainwright HDS implies that
$$
\frac{\sigma_\max(W)}{\sqrt{n}} \leq 1 + \delta + \sqrt{\frac{...
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Sampling from a hypersphere subject to a linear constraint? [duplicate]
I'm running into efficiency issues when trying to sample from a "hypercone" using rejection sampling. By a hypercone, I mean the set of vectors $C_{v,\beta} = \{w \sim N(0,1)\ |\ w^T v \geq \...
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The sum of $O_p$ --$ O_p \left(s^2\frac{\log d}{n}+s\sqrt{\frac{\log d}{n}} \right) $
I read papers in the area of inference for high-dimensional graphical models and these papers always state the convergence rate of the estimator. Using $O_p$ is a good choice.
Maybe I made some ...
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how to approximate the eigendecomposition of a correlation matrix when the data have been standardized?
Context
I am working to develop a penalized regression framework that will scale up to analyzing high dimensional data with a certain correlation structure. Let $X$ represent an $n \times p$ matrix of ...
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Wide Shallow Neural Networks VS Deep NN
I have several key points of understanding, but I cannot reach a final conclusion on why shallow neural networks cannot model data as effectively as deep neural networks.
I understand that we can ...
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Bound on Rademacher complexity using polynomial discrimination
This is lemma 4.14 in Wainwright's textbook on High-Dimensional Statistics, it states that given a class of function $\mathcal{F}$ has polynomial discrimination of order $v$, then for all integer $n$ ...
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High dimensional regression with millions of covariates/features
as a matter of preamble, I am a machine learning researcher. I am interested if this community can point me to research and work showing settings that have performed regression where the number of ...
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The covering number of a d-dim cube
In Martin Wainwright's textbook, equation (5.5) states that the $\delta$-covering number of the d-dimensional cube satisfies
$$
\log N(\delta; [0,1]^d) \asymp d \log(\frac{1}{\delta}),
$$
for small ...
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Should we routinely conduct unsupervised learning when reporting descriptive statistics on data?
A standard approach prior to conducting a predictive or inferential analysis is to report some basic univariate descriptive statistics on the study variables: mean, median, minimum, maximum, variance, ...
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What is the meaning of $\asymp$ and $\lesssim$ in Martin wainwright's high dim textbook? [closed]
Unfortunately, this text book did not provide a table of notations he used.
Can anyone provide me with a definition of $\asymp$ and $\lesssim$ and few examples?
For an example in the book, in display (...
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Modeling a high dimensional multicollinear data
I am trying to predict a Plant physiology trait (y) from hyper spectral reflectance data from 400 to 2400nm (X). So far i have done the following
Skew correction with Square root (sqrt) on y
Scaling ...
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Maximum Likelihood in High Dimensions [closed]
What are some examples of high-dimensional random variables for which MLE are solved using numerical methods because we are unable to explicitly solve the equations nicely? The only example to comes ...
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Large $N$, small $T$ in SUR: workaround using system GMM
Consider a system of linear equations as in seemingly unrelated regression (SUR). If the number of equations $N$ is large relative to the sample size $T$, the weighting matrix in SUR (i.e. the error ...
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Expected value of Cosinus in High dimension
I would like to prove that the cosinus of the angle formed by 3 randomly points tends to $\frac{1}{2}$ as the dimensionality tends to $\infty$. Could it be solved with the expected value formula ? It ...
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Benjamini Hochberg Procedure [closed]
I am working on a problem for class related to multiple testing where I would like to run the BH procedure with a known $\pi_{0}$, denoting the proportion of hypothesis that are truly null, given ...
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