# Questions tagged [projection]

For on-topic questions involving the mathematical concept projection, a linear transformation $P$ such that $P=P^2$. Please include also a more statistical methods tag. For purely mathematical questions about projections it is better to ask on math SE https://math.stackexchange.com/

62 questions
Filter by
Sorted by
Tagged with
14 views

### Whitening on projection matrices

The projection matrix $P = I -xx^T\in \mathbf{R}^{d \times d}$ has a zero eigenvalue and eigenvalues equal to one with multiplicity $d-1$. Is it possible to apply whitening transform on $P$ taking ...
28 views

### Project time series from previous time series examples and characteristics

Say I want to open a shop but first I want to project the likely sales in the first 5 years to see if it is a viable option. I have data pertaining to 100s of other start ups, including their success ...
29 views

### Question about Regression error and the residual maker matrix

Starting with the 'residual maker' defined by M in: $e= y-\hat{y} = Y-X(X'X)^{-1}X'Y = [I-X(X'X)^{-1}X']Y =MY$ where e is the regression residual. one common equality i see relating the regression ...
39 views

### Is $\hat \beta$ of general least squares an orthogonal projection?

$\hat \beta_{GLS} = (X'V^{-1}X)^{-1}X'V^{-1}Y \\ Y=X\hat \beta_{GLS} + \epsilon=X(X'V^{-1}X)^{-1}X'V^{-1}Y + \epsilon = \\X(X'V^{-1}X)^{-1}X'V^{-1}Y + (I-X(X'V^{-1}X)^{-1}X'V^{-1})Y$ It is clear that ...
12 views

### Neural ODEs, augmentation and subspace “projection”

The answer to the neural ODE question, the Augmented neural ODEs paper is mentioned. There, the following process happens: 2D data is augmented by padding with 1 zero 3D data is augmented once again ...
25 views

74 views

373 views

### Expected value as an orthogonal projection

I'm reading a paper in which the expected value of a random variable, $\mathbb{E}[X]$, is characterized as an orthogonal projection. This is on page 10. I've seen the geometric interpretation of ...
33 views

### Linear project when X includes a constant

In Hamilton's text I ran across the following statement: if $X$ includes a constant then the linear projection of $aY+b$ is $aP(Y\mid X)+b$ where $P(Y\mid X)$ is the linear projection of $y$ on $x$. I’...
149 views

### Linear regression with feature representation confusion - relationship of design matrix column space to the feature space?

I am trying to visualise the geometry of linear regression with feature representation. I have a regression problem with $n$ data pairs $\mathcal{D}:=\{(\mathbf{x},y)_{i}\}_{i=1}^{n}$, independent ...
303 views

### What's wrong with my solution to canonical correlation analysis (CCA) using the SVD

I am working through the derivations for solving CCA in A Tutorial on Canonical Correlation Methods. Right now, I am trying to solve CCA using SVD (bottom of page 95:7). For completeness, I include ...
1k views

### t-SNE, PCA and another technique - which one? [closed]

I am comparing dimension reduction techniques and I am utilizing them for data visualizations onto a plane – projections in 2D space. The input into a projection/dimension reduction techniques is a ...
207 views

### Conditional expectation and variable decomposition

Suppose that $X$ and $Y$ have an uknown joint distribution $f_{XY}$. How can I formally demostrate that it always exists a unique decomposition of the form : $$Y = E[Y|X] +\epsilon$$ without ...
17 views

### Model Selection - 6 month forecast given the past 25 months

As the title states, the problem at hand is asking me to predict the next 6 months values when given the past 25 months. In my opinion, the training data will be quite thin so traditional time series ...
34 views