Efficient Sequential Simulation-Based Inference Using Gaussian Locally Linear Mappings

Concetti Chiave

The author proposes a novel methodology for Bayesian inference using structured mixtures of probability distributions, providing accurate posterior inference with reduced computational demands.

Sintesi

The content discusses a novel approach to Bayesian inference using structured mixtures of probability distributions. The proposed method, SeMPLE, outperforms neural network-based methods in accuracy and efficiency across various benchmark models.

Simulation-based inference (SBI) bypasses the need for a likelihood function by considering a generative model or simulator. Recent methods have used neural networks to approximate likelihoods and posterior distributions. SeMPLE utilizes Gaussian Locally Linear Mapping (GLLiM) to provide accurate approximations for both likelihood and posterior distribution simultaneously. By incorporating an Expectation-Maximization algorithm within GLLiM, SeMPLE offers efficient posterior sampling in a tuning-free Metropolis-Hastings sampler. The method demonstrates superior performance in accuracy and resource efficiency compared to state-of-the-art neural network-based approaches like SNL and SNPE-C.

SeMPLE's resource requirements are significantly lower than traditional methods like SNL and SNPE-C, making it an efficient choice for Bayesian inference tasks. The approach leverages the power of structured mixtures of probability distributions to provide accurate posterior inference with minimal computational footprint. Overall, SeMPLE offers a frugal strategy that balances accuracy and computational efficiency in Bayesian inference tasks.

Statistiche

For Two Moons model:

SeMPLE requires 7.1 kJ and 0.71 GB for CPU+DRAM.
SNL requires 24.5 kJ and 19 GB for CPU+DRAM.
SNPE-C requires 15 kJ and 9 GB for CPU+DRAM.

For Hyperboloid model:

SeMPLE requires 3.2 kJ and 0.88 GB for CPU+DRAM.
SNL requires 54 kJ and 30 GB for CPU+DRAM.
SNPE-C requires 120 kJ and 15 GB for CPU+DRAM.

For Bernoulli GLM model:

SeMPLE requires 4.8 kJ and 0.93 GB for CPU+DRAM.
SNL requires 108 kJ and 75 GB for CPU+DRAM.
SNPE-C requires 41 kJ and 10 GB for CPU+DRAM.

For Ornstein-Uhlenbeck model:

SeMPLE requires 6.1 kJ and 0.93 GB for CPU+DRAM.
SNL requires 66 kJ and 39 GB for CPU+DRAM.
SNPE-C requires134 kJand15GBforCPU+DRAM.

Citazioni

"Our approach produces accurate posterior inference when compared to state-of-the-art NN-based SBI methods."
"SeMPLE shows low resource costs that are always of the same magnitude (<10kJand<1GB)."
"The runtime, energy, and memory requirementsforSeMPLEare considerably lower."

Approfondimenti chiave tratti da

Fast, accurate and lightweight sequential simulation-based inference using Gaussian locally linear mappings

by Henr... alle arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07454.pdf

Domande più approfondite

How does the use of structured mixtures of probability distributions improve the efficiency of Bayesian inference

The use of structured mixtures of probability distributions improves the efficiency of Bayesian inference in several ways. Firstly, these structured mixtures provide a more flexible and expressive way to model complex multivariate distributions compared to traditional methods. By incorporating multiple components with different weights and parameters, they can capture multimodalities and intricate patterns in the data more effectively.
Secondly, structured mixtures offer a balance between complexity and computational efficiency. Unlike neural network-based approaches that may require extensive tuning and training, structured mixtures often have fewer hyperparameters, making them easier to interpret and optimize. This simplicity leads to faster convergence during the learning process.
Additionally, by leveraging algorithms like Gaussian Locally Linear Mapping (GLLiM) within these mixture models, it becomes possible to obtain closed-form approximations for both likelihood functions and posterior distributions. This amortized approach allows for quick evaluations without repeated costly computations for each new observation or parameter setting.
Overall, the use of structured mixtures enhances the speed and accuracy of Bayesian inference by providing a versatile framework that efficiently captures the underlying complexities of real-world data while minimizing computational demands.

What are the implications of reducing computational demands while maintaining accuracy in statistical modeling

Reducing computational demands while maintaining accuracy in statistical modeling has significant implications across various domains:

Cost-Efficiency: Lower computational requirements translate into reduced costs associated with hardware resources such as processing power and memory storage. This cost-effectiveness is particularly beneficial when dealing with large datasets or complex models that would otherwise demand substantial computing resources.

Scalability: Models that are computationally efficient can be scaled up easily to handle larger datasets or more complex analyses without compromising on performance. This scalability enables researchers to tackle increasingly challenging problems without being limited by resource constraints.

Faster Decision-Making: Efficient statistical modeling allows for quicker turnaround times in generating insights from data analysis. Decision-makers can access timely information for strategic planning or operational improvements without delays caused by lengthy computation processes.

Improved Accessibility: Reduced computational demands make advanced statistical techniques accessible to a wider audience beyond experts in machine learning or statistics fields. Researchers from diverse disciplines can leverage sophisticated modeling tools for their research projects with minimal technical barriers.

5 .Environmental Impact: By optimizing computational workflows through efficiency gains, there is also a positive environmental impact due to lower energy consumption associated with running simulations or training models over extended periods.

How can the concept of amortization be applied more broadly in statistical learning methodologies

The concept of amortization can be applied more broadly in statistical learning methodologies across various areas:
1 .Parameter Estimation: In iterative optimization algorithms like Expectation-Maximization (EM) or Variational Inference (VI), previous computations could inform subsequent iterations rather than starting from scratch each time.
2 .Model Training: Neural networks could benefit from amortization by reusing learned representations across tasks instead of training separate models for each task.
3 .Hyperparameter Tuning: Amortizing hyperparameter search involves leveraging past experiments' results to guide future choices efficiently.
4 .Sequential Learning: Sequential methods like Active Learning could utilize past observations' knowledge when selecting new samples for labeling.
5 .Bayesian Inference: Amortized inference techniques such as Automatic Differentiation Variational Inference (ADVI) aim at approximating posteriors once using neural networks then applying them repeatedly on new data points quickly.
By incorporating amortization strategies into these methodologies, practitioners can achieve faster convergence rates during model training/inference processes while reducing redundant computations significantly leading towards more efficient utilization of resources overall