Analyses are underdetermined when the number of parameters to be estimated is greater than the number of data. This problem is also referred to as 'p >> n'.

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17
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5answers
2k views

Detecting significant predictors out of 300 independent variables

In a dataset of two non-overlapping populations (patients & healthy, total $n=60$) I would like to find (out of $300$ independent variables) significant predictors for a continuous dependent ...
11
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4answers
2k views

Minimum sample size for PCA when the main goal is to estimate the first or second principal component?

If I have a dataset with $n$ observations and $p$ variables (dimensions), and generally $n$ is small (n=12-16), and $p$ may range from small (p = 4-10) or perhaps much larger (p= 30-50). I remember ...
4
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1answer
718 views

Feature selection & model with glmnet on Methylation data (p>>N)

I would like to use GLM and Elastic Net to select those relevant features + build a linear regression model (i.e., both prediction and understanding, so it would be better to be left with relatively ...
4
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2answers
108 views

Why is it bad if number of dimensions / factors > sample size?

I've been told (read) this many times, but I never understood why it's bad for the number of dimensions in your data, or the number of explanatory variables in your model to be higher than your ...
2
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3answers
179 views

SVM has relatively low classification rate for high-dimensional data even though 2-D projections show they are separable

I have another problem with 14000 features and 500 training samples. It is a binary classification problem and approximately in the form of an ellipse. My classification accuracy using the 2nd degree ...
2
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1answer
113 views

Applying ridge regression for an underdetermined system of equations?

When $y = X\beta + e$, the least squares problem which imposes a spherical restriction $\delta$ on the value of $\beta$ can be written as \begin{equation} \begin{array} &\operatorname{min}\ \| y - ...
2
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0answers
49 views

Interpretation of regression coefficients obtained from applying left inverse of regressor matrix in an underdetermined system?

If $X^\dagger$ is the pseudo-inverse of $X$, $\beta = X^\dagger y$ is the least squares solution for $\beta$ when $y=X\beta$. In the overdetermined case, applying $X^{\dagger,L} = (X^TX)^{-1}X^T$ ...
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1answer
43 views

Dealing with underdetermination in Bayesian models

Bayesian models are supposedly well equipped to deal with high-dimensionality problems, and can handle sparse data well, too. But suppose I've created a model that estimate more parameters than there ...
1
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0answers
26 views

How to test for differences between groups over time when N is less than the number of levels

I have done a live cell imaging time course over 24 hours, and have a result for each hour. I have 3 experimental groups and 1 control group. What I want to know is if any of the experimental groups ...