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Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics - solving scale-imbalanced neural data analysis
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基于 SOC 职业分类
| name | computation-aware-kalman-neural-dynamics |
| description | Computation-Aware Kalman Filtering with Model Selection for Neural Dynamics - solving scale-imbalanced neural data analysis |
| version | 1 |
| category | neuroscience |
| activation_keywords | ["neural dynamics","Kalman filtering","Bayesian inference","model selection","uncertainty quantification","computational uncertainty","latent variable model","neural recording","state-space model"] |
| created | 2026-06-06T00:00:00.000Z |
| paper_id | arXiv:2606.01468 |
| authors | JR Huml, Jonathan Wenger, John P. Cunningham |
| venue | 2nd International Conference on Probabilistic Numerics (2026) |
Problem: Modern neural datasets (single-cell recordings) are scale-imbalanced - fewer trials than recorded neurons. Bayesian methods model uncertainty well but scale poorly; deep networks scale well but lack uncertainty quantification.
Solution: Computation-Aware State-Space Model (CASSM) - extends computational uncertainty to model selection with novel training loss and optimization scheme.
Key Innovation: Tractable inference in large state-spaces while maintaining uncertainty calibration - competitive with data-hungry deep networks but with principled Bayesian framework.
# Conceptual framework
class CASSM:
"""
Computation-Aware State-Space Model for Neural Dynamics
Key Components:
1. Latent state dynamics: z_t = f(z_{t-1}) + noise
2. Observation model: y_t = g(z_t) + noise
3. Computational uncertainty: accounts for approximation error
4. Model selection: adaptive hyperparameter optimization
"""
def __init__(self, n_neurons, n_trials, state_dim):
self.scale_imbalanced = n_trials < n_neurons
self.state_dim = state_dim
self.computational_budget = estimate_complexity(n_neurons, state_dim)
def inference(self, observations):
# Computation-aware filtering
state_posterior, uncertainty = kalman_with_computational_error(
observations,
computational_budget=self.computational_budget
)
return state_posterior, uncertainty
| Method | Accuracy | Uncertainty Calibration | Scalability |
|---|---|---|---|
| Standard Kalman | Medium | High | Poor (O(n²)) |
| Deep Networks | High | None | Good |
| CASSM | High | High | Medium-Good |
✓ Scale-imbalanced regime (n_trials < n_neurons) ✓ Need uncertainty quantification (confidence intervals, hypothesis testing) ✓ Limited computational budget (need efficiency) ✓ Model selection uncertainty (hyperparameter tuning)
✗ Data-rich regime (n_trials >> n_neurons) - use standard methods ✗ No uncertainty needed - use simpler deep networks ✗ Small state dimension - computational error negligible
import numpy as np
from scipy.linalg import block_diag
class ComputationAwareKalman:
def __init__(self, n_neurons, state_dim, trials):
self.n_neurons = n_neurons
self.state_dim = state_dim
self.trials = trials
self.scale_imbalanced = trials < n_neurons
def estimate_computational_budget(self):
"""
Estimate computational cost for given state dimension
Returns: flops, memory requirements
"""
flops = self.state_dim**2 * self.trials
memory = self.state_dim * self.n_neurons
return flops, memory
def model_selection_loss(self, theta, data, lambda_comp=0.1):
"""
Novel training loss balancing prediction and computation
theta: model parameters
lambda_comp: computational penalty weight
"""
# Prediction error
log_likelihood = self.compute_log_likelihood(theta, data)
# Computational error
comp_error = self.estimate_computational_error(theta)
# Combined loss
loss = -log_likelihood + lambda_comp * comp_error
return loss
Primary Paper:
Related Work:
Core Idea: Bayesian neural dynamics modeling with computational uncertainty + model selection
Best Use Case: Scale-imbalanced neural data (few trials, many neurons)
Key Advantage: Principled uncertainty with modern scalability
Main Method: Computation-aware Kalman filtering + novel training loss
Validation: Competitive accuracy, superior uncertainty calibration
Activation Keywords: neural dynamics, Kalman filtering, Bayesian inference, model selection, uncertainty quantification, computational uncertainty, latent variable model, neural recording, state-space model
Related Skills: neural-population-dynamics, latent-dynamics-modeling, kalman-filtering-neural-data, bayesian-neural-modeling