# Efficient and principled score estimation with Nystr"om kernel exponential families

arXiv: https://arxiv.org/abs/1705.08360 · HTML: https://mlsanity.com/paper/1705.08360/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2017.

## Built on by (most cited first, 9 of 9)

- [A Computationally Efficient Method for Learning Exponential Family Distributions](https://mlsanity.com/paper/2110.15397/) (2021)
- [Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression](https://mlsanity.com/paper/2305.00608/) (2023)
- [Wavelet Transform-assisted Adaptive Generative Modeling for Colorization](https://mlsanity.com/paper/2107.04261/) (2021)
- [Exponential Family Model-Based Reinforcement Learning via Score Matching](https://mlsanity.com/paper/2112.14195/) (2021)
- [MARS: Meta-Learning as Score Matching in the Function Space](https://mlsanity.com/paper/2210.13319/) (2022)
- [Active Slices for Sliced Stein Discrepancy](https://mlsanity.com/paper/2102.03159/) (2021)
- [Conditionally Strongly Log-Concave Generative Models](https://mlsanity.com/paper/2306.00181/) (2023)
- [Denoising Score Matching with Random Fourier Features](https://mlsanity.com/paper/2101.05239/) (2021)
- [Kernel Deformed Exponential Families for Sparse Continuous Attention](https://mlsanity.com/paper/2111.01222/) (2021)

## Abstract (arXiv)

We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite-dimensional. The model is learned by fitting the derivative of the log density, the score, thus avoiding the need to compute a normalization constant. Our approach improves the computational efficiency of an earlier solution by using a low-rank, Nystr"om-like solution. The new solution retains the consistency and convergence rates of the full-rank solution (exactly in Fisher distance, and nearly in other distances), with guarantees on the degree of cost and storage reduction. We evaluate the method in experiments on density estimation and in the construction of an adaptive Hamiltonian Monte Carlo sampler. Compared to an existing score learning approach using a denoising autoencoder, our estimator is empirically more data-efficient when estimating the score, runs faster, and has fewer parameters (which can be tuned in a principled and interpretable way), in addition to providing statistical guarantees.