模型拟合的贝叶斯自适应直接搜索 (BADS) 优化算法附matlab代码.zip

# Bayesian Adaptive Direct Search (BADS) - v1.0.8 **News:** - If you are interested in Bayesian model fitting, check out [Variational Bayesian Monte Carlo (VBMC)](https://github.com/lacerbi/vbmc), a simple and user-friendly toolbox for Bayesian posterior and model inference that we published at NeurIPS (2018, 2020). - The BADS paper [[1](#reference)] has been accepted for a poster presentation at [NeurIPS 2017](https://papers.nips.cc/paper/6780-practical-bayesian-optimization-for-model-fitting-with-bayesian-adaptive-direct-search)! (20.9% acceptance rate this year, for a total of 3240 submissions) - BADS has also been presented at the NeurIPS workshop on Bayesian optimization for science and engineering, [BayesOpt 2017](https://bayesopt.github.io/). ## What is it BADS is a novel, fast Bayesian optimization algorithm designed to solve difficult optimization problems, in particular related to fitting computational models (e.g., via [maximum likelihood estimation](https://en.wikipedia.org/wiki/Maximum_likelihood_estimation)). BADS has been intensively tested for fitting behavioral, cognitive, and neural models, and is currently being used in many computational labs around the world. In our benchmark with real model-fitting problems, BADS performed on par or better than many other common and state-of-the-art MATLAB optimizers, such as `fminsearch`, `fmincon`, and `cmaes` [[1](#reference)]. BADS is recommended when no gradient information is available, and the objective function is non-analytical or *noisy*, for example evaluated through numerical approximation or via simulation. BADS requires no specific tuning and runs off-the-shelf like other built-in MATLAB optimizers such as `fminsearch`. If you are interested in estimating posterior distributions (i.e., uncertainty and error bars) over parameters, and not just point estimates, you might want to check out [Variational Bayesian Monte Carlo](https://github.com/lacerbi/vbmc), a toolbox for Bayesian posterior and model inference which can be used in synergy with BADS. ## Installation [**Download the latest version of BADS as a ZIP file**](https://github.com/lacerbi/bads/archive/master.zip). - To install BADS, clone or unpack the zipped repository where you want it and run the script `install.m`. - This will add the BADS base folder to the MATLAB search path. - To see if everything works, run `bads('test')`. ## Quick start The BADS interface is similar to that of other MATLAB optimizers. The basic usage is: ```matlab [X,FVAL] = bads(FUN,X0,LB,UB,PLB,PUB); ``` with input parameters: - `FUN`, a function handle to the objective function to minimize (typically, the *negative* log likelihood of a dataset and model, for a given input parameter vector); - `X0`, the starting point of the optimization (a row vector); - `LB` and `UB`, hard lower and upper bounds; - `PLB` and `PUB`, *plausible* lower and upper bounds, that is a box where you would expect to find almost all solutions. The output parameters are: - `X`, the found optimum. - `FVAL`, the (estimated) function value at the optimum. For more usage examples, see [**bads_examples.m**](https://github.com/lacerbi/bads/blob/master/bads_examples.m). You can also type `help bads` to display the documentation. For practical recommendations, such as how to set `LB` and `UB`, and any other question, check out the FAQ on the [BADS wiki](https://github.com/lacerbi/bads/wiki). *Note*: BADS is a *semi-local* optimization algorithm, in that it can escape local minima better than many other methods — but it can still get stuck. The best performance for BADS is obtained by running the algorithm multiple times from distinct starting points (see [here](https://github.com/lacerbi/bads/wiki#how-do-i-choose-the-starting-point-x0)). ## How does it work BADS follows a [mesh adaptive direct search](http://epubs.siam.org/doi/abs/10.1137/040603371) (MADS) procedure for function minimization that alternates **poll** steps and **search** steps (see **Fig 1**). - In the **poll** stage, points are evaluated on a mesh by taking steps in one direction at a time, until an improvement is found or all directions have been tried. The step size is doubled in case of success, halved otherwise. - In the **search** stage, a [Gaussian process](https://en.wikipedia.org/wiki/Gaussian_process) (GP) is fit to a (local) subset of the points evaluated so far. Then, we iteratively choose points to evaluate according to a *lower confidence bound* strategy that trades off between exploration of uncertain regions (high GP uncertainty) and exploitation of promising solutions (low GP mean). **Fig 1: BADS procedure**  See [here](https://github.com/lacerbi/optimviz) for a visualization of several optimizers at work, including BADS. See our paper for more details [[1](#reference)]. ## Troubleshooting If you have trouble doing something with BADS: - Check out the FAQ on the [BADS wiki](https://github.com/lacerbi/bads/wiki); - Contact me at <luigi.acerbi@helsinki.fi>, putting 'BADS' in the subject of the email. This project is under active development. If you find a bug, or anything that needs correction, please let me know. ## BADS for other programming languages BADS is currently available only for MATLAB. A Python version is being planned. If you are interested in porting BADS to Python or another language (R, [Julia](https://julialang.org/)), please get in touch at <luigi.acerbi@helsinki.fi> (putting 'BADS' in the subject of the email); I'd be willing to help. However, before contacting me for this reason, please have a good look at the codebase here on GitHub, and at the paper [[1](#reference)]. BADS is a fairly complex piece of software, so be aware that porting it will require considerable effort and programming skills. ## Reference 1. Acerbi, L. & Ma, W. J. (2017). Practical Bayesian Optimization for Model Fitting with Bayesian Adaptive Direct Search. In *Advances in Neural Information Processing Systems 30*, pages 1834-1844. ([link](https://papers.nips.cc/paper/6780-practical-bayesian-optimization-for-model-fitting-with-bayesian-adaptive-direct-search), [arXiv preprint](https://arxiv.org/abs/1705.04405)) You can cite BADS in your work with something along the lines of > We optimized the log likelihoods of our models using Bayesian adaptive direct search (BADS; Acerbi and Ma, 2017). BADS alternates between a series of fast, local Bayesian optimization steps and a systematic, slower exploration of a mesh grid. Besides formal citations, you can demonstrate your appreciation for BADS in the following ways: - *Star* the BADS repository on GitHub; - [Follow me on Twitter](https://twitter.com/AcerbiLuigi) for updates about BADS and other projects I am involved with; - Tell me about your model-fitting problem and your experience with BADS (positive or negative) at <luigi.acerbi@helsinki.fi> (putting 'BADS' in the subject of the email). ### License BADS is released under the terms of the [GNU General Public License v3.0](https://github.com/lacerbi/bads/blob/master/LICENSE.txt).