# Multiplying by E[xy'] where only some statistics of xy' are known

Computational Science Asked by Yaroslav Bulatov on October 7, 2020

(cross-posted on crossvalidated)

For random variable $$(x,y)$$ in $$mathbb{R}^{d}times mathbb{R}^{d}$$ and vector $$v in mathbb{R}^d$$, I need to perform the following matrix vector multiplication.

$$T(v)=E[xy’]v$$

The issue is that the expected matrix $$E[xy’]$$ is too large to represent in memory ($$dapprox$$1 million), so I can only afford to store $$O(d)$$ worth of statistics and perform $$O(d^{1.5})$$ worth of operations. Three such statistics are $$E[x]$$, $$E[y]$$ and $$E[xodot y]$$, where $$odot$$ refers to element-wise multiplication.

If I only had the first two, one could argue that the following modification of $$T$$ is appropriate, representing an unbiased guess subject to these constraints

$$T(v)approx E[x]E[y’]v$$

What’s an appropriate way to incorporate $$E[xodot y]$$?

## Related Questions

### Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

0  Asked on August 29, 2021

### How avoid square shape with Laplacian operator in reaction diffusion calculations?

1  Asked on August 28, 2021

### traction boundary conditions in elasticity

1  Asked on August 28, 2021

### What’s the simplest way to graph a 2d array generated in C++ using Windows 7?

4  Asked on August 27, 2021 by hair-of-slytherin

### How is the final result calculated in RK-Dopri(4,5)?

1  Asked on August 26, 2021

### Optimization of expensive model with many parameters

2  Asked on August 26, 2021

### Flux sign and face normal confusion in finite volume method

3  Asked on August 24, 2021

### Computation of a functional for large values

0  Asked on August 22, 2021

### Which scheme for inhomogeneous convection-diffusion equation with highly variable coefficients?

1  Asked on August 22, 2021 by kieransquared

### interface value on the error equation

1  Asked on August 22, 2021

### Uniaxial stretching solution not uniform in FEM code

2  Asked on August 22, 2021

### Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

1  Asked on August 22, 2021 by eleuname

### Random access random permutations

1  Asked on August 22, 2021 by geoffrey-irving

### Looking for Runge-Kutta 8th order in C/C++

4  Asked on August 22, 2021

### Constructing explicit Runge Kutta methods of order 9 and higher

2  Asked on August 22, 2021

### In FEM, why is the stiffness matrix positive definite?

2  Asked on August 22, 2021

### Parabolic differential equations with time delay

1  Asked on August 22, 2021 by lcfactorization

### Numerically finding constants of motion

3  Asked on August 22, 2021

### Numerical packages to solve Volterra integral equations

1  Asked on August 22, 2021

### coupled equations with finite difference method

1  Asked on August 22, 2021 by m-douglas