1
vote
0answers
145 views

Incoherence of the row/column span

Due to V.Chandrasekaran., et al‎ (p.11) : In general for any $k$-dimensional subspace of $A_{n×n}$ we have that: $$\sqrt{(k/n)} \leq incoherence(A)\leq 1$$ where the lower bound is achieved (for ...
1
vote
2answers
505 views

Choice of Lipschitz constant for proximal gradient optimization

I'm trying to use proximal gradient methods (Forward-Backwards Splitting and FISTA) to minimize a function $f(B) = \frac{1}{2}|| XB - Y||_F^2 + \frac{\gamma}{2}||B C^T||_F^2$, where $X \in ...
2
votes
2answers
305 views

My overdetermined linear system gives both bad and good estimates. Why ?

Hello to everyone. What the question means is that different ways of expressing the same relation between the data and unknown variables produce really weird fit results: The problem: I have the ...
2
votes
1answer
264 views

Point-wise error estimate in polynomial regression

In our application we wish to estimate the actual path of objects. We have a set of samples of object locations $(t_i, x_i, y_i, P_i)$ where $t_i$ is the sample time, $(x_i, y_i)$ is the 2D location, ...
5
votes
1answer
296 views

Approximating a probability distribution by a mixture

Let us consider a probability distribution $(g_n)_{n \in \mathbb{N}}$ which we want to approximate by a mixture of $(f_n(\lambda))_{n \in \mathbb{N}}$ where $\lambda \in \mathbb{R}$ is a parameter. ...
6
votes
1answer
682 views

Random, Linear, Homogeneous Difference Equations and Time Integration Methods for ODEs

Most methods (that I know of) of numerically approximating the solution of ODEs are "general linear methods". For this type of method, the so-called 'linear stability' is examined by applying the ...
0
votes
2answers
520 views

univariate prior corresponding to weighted sum of L1 and L2 penalties?

Is there a univariate probability distribution $p_{\lambda,\alpha}(\beta)$ over the reals, parameterized by $\lambda > 0$ and $1 >= \alpha >= 0$, such that $p_{\lambda,\alpha} \propto ...