# Deep Random Splines for Point Process Intensity Estimation of Neural Population Data

arXiv: https://arxiv.org/abs/1903.02610 · HTML: https://mlsanity.com/paper/1903.02610/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2019.

## Built on by (most cited first, 8 of 8)

- [Neural Latents Benchmark '21: Evaluating latent variable models of neural population activity](https://mlsanity.com/paper/2109.04463/) (2021)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [Drop, Swap, and Generate: A Self-Supervised Approach for Generating Neural Activity](https://mlsanity.com/paper/2111.02338/) (2021)
- [Learning Behavior Representations Through Multi-Timescale Bootstrapping](https://mlsanity.com/paper/2206.07041/) (2022)
- [Nonparametric Automatic Differentiation Variational Inference with Spline Approximation](https://mlsanity.com/paper/2403.06302/) (2024)
- [TR0N: Translator Networks for 0-Shot Plug-and-Play Conditional Generation](https://mlsanity.com/paper/2304.13742/) (2023)
- [Amortized Variational Inference of Latent Intensities from Replicated Point Patterns](https://mlsanity.com/paper/2610.16669/) (2026)

## Abstract (arXiv)

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by transforming Gaussian noise through a deep neural network whose output are the parameters of a spline. Unlike Gaussian processes, Deep Random Splines allow us to readily enforce shape constraints while inheriting the richness and tractability of deep generative models. We also present an observational model for point process data which uses Deep Random Splines to model the intensity function of each point process and apply it to neural population data to obtain a low-dimensional representation of spiking activity. Inference is performed via a variational autoencoder that uses a novel recurrent encoder architecture that can handle multiple point processes as input. We use a newly collected dataset where a primate completes a pedaling task, and observe better dimensionality reduction with our model than with competing alternatives.