# Sampling from Arbitrary Functions via PSD Models

@inproceedings{MarteauFerey2022SamplingFA, title={Sampling from Arbitrary Functions via PSD Models}, author={Ulysse Marteau-Ferey and Francis R. Bach and Alessandro Rudi}, booktitle={AISTATS}, year={2022} }

In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through evaluations of the density, current methods either scale badly with the dimension or require involved implementations. Instead, we take a two-step approach by first modeling the probability distribution and then sampling from that model. We use the recently…

## 3 Citations

### PSD Representations for Effective Probability Models

- Computer Science, MathematicsNeurIPS
- 2021

This work characterize both approximation and generalization capabilities of PSD models, showing that they enjoy strong theoretical guarantees and can perform both sum and product rule in closed form via matrix operations, enjoying the same versatility of mixture models.

### SECOND ORDER CONDITIONS TO DECOMPOSE SMOOTH FUNCTIONS AS SQUARES

- Mathematics, Computer Science
- 2022

Second order suﬃcient conditions in order for a p times continuously diﬀerentiable non-negative function to be a sum of squares of p − 2 di-erentiable functions are shown, showing that, locally, the function grows quadratically in directions which are orthogonal to its set of zeros.

### Second order conditions to decompose smooth functions as sums of squares

- Mathematics, Computer Science
- 2022

Second order sufficient conditions are shown in order for a p times continuously differentiable non-negative function to be a sum of squares of p− 2 differentiable functions and it is shown that, locally, the function grows quadratically in directions which are orthogonal to its set of zeros.

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