# Questions tagged [underdetermined]

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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### Wide feature matrix but few examples

I have a data set of 125, with only about 25 (20%) positive cases. The features, lets call them Feature1, Feature2 up to Feature250, can be easily grouped (since they all describe responses to ...
28 views

### Appropriate dimensionality reduction technique for a small, but high-dimensional sample

I am attempting to conduct some multivariate analysis on a dataset I've been given with a sample size (n) of 23 and a feature number (p) of ~800. I would like to use dimensionality reduction, but ...
40 views

### Best estimate of underdetermined system using prior

I have measured two variables which depend on the same set of four parameters. I want to know the parameters which best explain my measurements. Of course, I cannot solve for four unknowns from just ...
112 views

### Linear discriminant analysis with $p\gg n$

I am studying Linear Discriminant Analysis (LDA). According to the formula for LDA, we are supposed to get the inverse of within group covariance. However, if $p\gg n$ (i.e., the dimension is much ...
3k views

### Can one (theoretically) train a neural network with fewer training samples than weights?

First of all: I know, there is no general number of sample size required to train a neural network. It depends on way too many factors like complexity of the task, noise in the data and so on. And the ...
632 views

### Why is $n < p$ a problem for OLS regression?

I realize I can't invert the $X'X$ matrix but I can use gradient descent on the quadratic loss function and get a solution. I can then use those estimates to calculate standard errors and residuals. ...
163 views

### Fitting least squares when number of predictors are larger than instances

A statement from the book Introduction to Statistical learning with applications in R, didn't quite make sense to me. It says, "In cases when number of predictors are greater than the instances we ...
829 views

### How to identify a SEM with formative dependent variable (with R's lavaan package)?

I have a formative construct in a structural equation model (SEM) which I would like to estimate with the function sem in the ...
771 views

### Do I have too many variables and not enough data points for cluster analysis?

I have 75 observations and 152 variables. I want to perform cluster analysis. If I perform cluster analysis and this data will the results be meaningful? Do I need to reduce the number of variables ...
398 views

### LASSO prediction model question

I am trying to create a prediction model with 33 predictors (brain metabolite levels in various regions) and 8 observations (cognitive test scores) with p>>n problem using LASSO in MATLAB (...
2k views

### Solving a practical machine learning problem

I am currently doing my Phd in computational biology at Stanford. I get the data I need to answer the questions I am interested in. The data sets are sometimes "large" and these large problems take ...
162 views

### Dataset for Least Angle Regression

I have read that least angle regression is good for high dimensional data. I didn't actually understand the meaning of high dimensional data, so does this mean $p>>n$ case? And does anyone know ...
3k 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 - ...
224 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 $X^{\dagger,L} = (X^TX)^{-1}X^T$ ...
223 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 ...
21k 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 ...
3k 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 ...
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 ...