Questions tagged [bayesian-optimization]

Bayesian optimization is a family of global optimization methods which use information about previously-computed values of the function to make inference about which function values are plausibly optima. Its applications include computer experiments and hyper-parameter optimization in some machine learning models.

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Expected Improvement formula for Bayesian Optimisation

The expected improvement on how to choose a next point $x$ for evaluation is to choose the point such that $$arg\,max_{x}E[f(x) - f^{max}]$$ where $f(x)$ denotes the gaussian process posterior ...
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Elementary explanation of Gaussian Processes

I'm learning of Gaussian Processes (GP) in the context of Bayesian Optimization (BO), where a surrogate function is learned to approximate the reward signal then a (hopefully) global optima is ...
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Bayesian hyperparameter optimization, is it worth it?

On Goodfellow-et-al-2016,Deep Learning book the following sentence can be found: "Currently, we cannot unambiguously recommend Bayesian hyperparameter optimization as an established tool for ...
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Who first proposed Bayesian optimisation with Gaussian processes?

From what I understand, the 'standard' approach to Bayesian Optimisation uses a Gaussian process for the prior (as opposed to more recent proposals like TPE or Bayesian Optimisation with random ...
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Optimize learning rate of boosting algorithms efficiently with hyperopt

I've been exploring the hyperopt python library to tune parameters for boosting algorithms. Learning rate is one of the focal parameters for which efficient tuning appears more difficult. My ...
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Binary classification, imbalanced dataset optimization: AUC vs logloss

I'm running optimization on an imbalanced dataset and need to define my optimization metric. I'm working on disease detection so maximizing AUC might not be the best solution, as the certainty of the ...
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Maximising the utility when I have a large number of discrete decisions mixed with continuous decisions

I have an optimisation problem which is potentially quite tricky. Consider the problem of allocating a discrete number of resources (in my case, they are spare mechanical components for a large ...
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32 views

Optimizing Equation involving CDF and PDF

Assume you have two random variables, $v_b \sim N(\mu_b,\sigma_b^2)$ and $v_s \sim N(\mu_s,\sigma_s^2)$ and let $\rho$ be the correlation between them. Denote by $F$ and $f$ the CDF and PDF of the ...
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Using Bayesian methods for experimental design

I'm trying to determine parameters for a function. After a given number of (computational) experiments the retrieved data is used for doing a fitting and the parameters are then obtained. (...
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Black-box optimization algorithms performance

I've been doing some basic research of the black-box optimization algorithms that are on the market (and have Python implementation). I've found some recent and promising algorithms like LIPO, SHGO or ...
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Bayesian optimization experiment to confirm learning rate schedules in DNNs

Common learning rate schedules usually decrease the learning based on some criteria or some predefined schedule which intuitively makes sense. Has it been confirmed with bayesian hyper parameter ...
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Why not use large ($n - [n^{0.75}]$) validation sets in machine learning training loop?

I am seeking feedback in the form of answers to a bold question. Please limit comments to requests for clarification of the question only. There appears to be an influence on machine learning ...
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Bayesian optimization with xgb.cv and xgb.XGBClassifier - Mismatch between AUC scores

I'm doing bayesian hyperparameter optimization with bayes_opt and maximizing the AUC. I'm noticing a big discrepancy between the cross-validation scores that I ...
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Bayesian optimisation to find a function that satisfies some constraints

Am new to Bayesian optimisation and am trying to apply it to a research problem I am working on. General introductory literature to Bayesian optimisation suggests that we can use it to find the ...
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How to ensure inequality constraints on surrogate model from Bayesian optimization?

I am using bayesian optimization as a sequential strategy to globally optimize my objective function on a Simplex. Currently I am using Gaussian Process Regression for my surrogate model. Gaussian ...
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37 views

Low rank plus diagonal approximation of covariance of model parameters

In this paper regarding Bayesian Deep Learning, in Section 3.4, the authors want to approximate the covariance of a distribution over the model parameters $\theta$. They first get an estimate of the ...
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Is Bayesian approach the correct way to solve this problem?

I have a dataset that has 4 variables and the target is a value between 1 to 5. this data is generated from an api that is black box and I don't know the formula that generates these values. I have ...
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29 views

Reduce search space for hyperopt

I am using the model SVR to create a regression model. This class contains several hyperparameters, and to try to find the best ones according to the several features, I am using the library hyperopt. ...
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Experimental design for optimizing a machine producing candles [duplicate]

I have the following problem that I would like to solve, but I don't know where to look. I have a Machine A that produces candles. According to the pre-setting of the machine, the color, the height, ...
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Bayesian estimation difference between inferences is conjugate prior and non informative prior [duplicate]

What are the differences in the inferences using non-informative (specifically Jeffrys) priors as compared to the conjugate prior?
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Optimization of hyperparameters and parameters

As far as I understand, in Machine Learning there are 2 moments for optimization. Before training the model there is the optimization of the hyperparameters to find the best configuration of the model ...
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What is the most efficient algorithm for hyper-parameter optimization, specially when comparing Bayesian optimisation and evolutionary algorithms?

I've been reading some papers about how Bayesian optimisation has achieved great results in hyper-parameter tuning when compared with random search or grid search. What about when comparing with ...
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Understanding concrete dropout

I am trying to understand a technique call Concrete Dropout for automatically tuning the dropout rate during the network training. However, I am unable to follow the work described in the paper ...
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Bayesian estimation for analysing project evaluation

Using Bayesian estimation how can we assess the group projects given that different members in the group may have performed differently?
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How to change priors in Bayesian estimation, if we get to know previous work was wrong?

Assuming we are doing a task to find how runs will be scored some match and for that, we have assumed some prior, now what if we find out midway through the process on which we built our priors was ...
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Why does my Gibbs sampler find two optimals?

[EDITED] I am using a Gibbs Sampler to find a Bayesian optimization to my multilevel (hierarchical) model (2 levels). However, when I run multiple chains (each chain having different starting values) ...
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Bayesian optimization with offline stochastic function and sticky decisions

Is there a bayesian optimization (BO) framework which allows: 1. Warm start with offline data 2. Stochastic function f(x) is noisy 3. Every iteration is n samples controlled by agent and there are ...
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why in Gaussian linear regression they put $y_i-\theta^Tx_i$ instead of $x$?

I am new to the machine learning area. Then I am studying a paper that considers the problem of logistic regression in Bayesian. In general, in regression or logistic regression when they assume the ...
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Expected improvement compared with probability of improvement and lower confidence bound [closed]

From all the references i read so far, i have been seeing Expected improvement being commonly used as acquisition function. Why is that so, compared with the other two i mentioned in the title/...
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Is sampling the training set for hyperparameter optimisation a good speed up solution?

I am using Bayesian hyperparameter optimization for LSTM hyperparameters. This manages to find an optimum set of hyperparameters in much fewer iterations than a grid search. My problem is that I ...
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What is the “tree” structure in Tree Parzen Estimators?

Context In Algorithms for Hyper-Parameter Optimization, the authors propose a "tree-structured" configuration space. Here, a configuration space is a space of hyperparameters. Questions What ...
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tradeoff function for exploration/exploitation in the context of gaussian process bayesian optimisation

First, let's give some context to my issue: consider an objective function $f(x)$ defined over a compact set $D$, such that there exists $x^*, f(x^*) > f(x) \quad \forall x \in D$. My goal is to ...
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Undersampling strategy as part of Bayesian optimization

I am using gp_minimize from skopt for the optimization of my model, which I then plug into ...
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1answer
111 views

Optimization problem with recursive functions

I could image that the following is a standard optimization problem but nevertheless I have no clue how to specifically solve it: by which specific approach, algorithm, and which computing powers I ...
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Optimizing hyperparameters of network with extremely long training time

As an example, let's say i am using a very deep fully convolutional autoencoder to segment lung scans. Input image resolutions will be large, since the features i hope to segment (things like early ...
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What is the current highest dimension for efficient Bayesian Optimization

It is frequently stated that BO can only be efficient for under 10 dimensions, or thereabouts. By efficient, I mean that the optimum is reached in an acceptable time, say less than a day given all ...
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206 views

acquisition function for bayesian optimisation using random forests as surrogate model

I'm working on implementing a Bayesian optimization class in Python. As a surrogate model, I used a Gaussian process until now. From what I read it's quite standard as it is efficient and intuitive. ...
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180 views

random forest regression with uncertainty output [closed]

For a Bayesian optimization problem, I wish to use a random forest regressor in Python, able to predict for unseen data a probability distribution, like in the paper Decision Forests for ...
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67 views

Gaussian Process - The variance term in Kernel matrix is not reducing to 0 at the Location of the Data Point

I am running a variance reduction experiment using GPy library and sampling using Bayesian optimization suggested location. I noticed that once the data at certain location is added to GP's data set, ...
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What is the actual distribution that we are modelling in case of a Bayesian Regression Model?

I have come across blog posts that speak about modelling a regression problem using Bayesian approaches. I completely understand that, to set up example data, they generate a sine wave using a one ...
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1answer
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Using probabilistic scores in Bayesian Optimisation

I was reading up on Bayesian Optimization and in one of the articles, I came across the following passage. We could just use the surrogate score directly. Alternately, given that we have chosen a ...
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Why are frequentists uncomfortable with bayesian statistics when “optimization” algorithms used in frequentist statistics is bayesian?

In Step 1, we have a prior. Using bayes rule we construct the posterior. In step 2 of some iterated bayesian procedure, the prior becomes the posterior from step one and use bayes rule to calculate ...
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82 views

Multi armed bandits with natural ordering between bandits

Say I have a button in my website that I want to optimize the size given some metric. In order to use multi armed bandits for that, there are some things I would like to consider: My metric is a ...
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1answer
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Is expected improvement acquisition function in Bayesian optimization a Gaussian process?

So I know there are several types of acquisition function for Bayesian optimization technique. But according to Wikipedia There are several methods used to define the prior/posterior distribution ...
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268 views

Difference between Bayesian Optimization and Bayesian Statistical Inference [closed]

Can someone give a lucid explanation pointing out how are Bayesian Optimization and Bayesian Statistical Inference different to each other? Can they be seen as complementary to each other or are they ...
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How can one optimize black-box functions given context?

Libraries like hyperopt or scikit-optimize allow one to optimize a black-box function. However, they do not allow specifying contextual information outside of the parameters to be chosen by the ...
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75 views

What do we want to maximize in hyperparameter tuning with bayesian optimization?

So I am trying to implement Bayesian optimization for various machine learning methods, all of then consist of hyperparameters which should be tuned (eg. complexity parameter, minimum samples in split ...
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1answer
138 views

How to estimate the error of the model in the best way?

I have many samples in my data and I want to fit many models which should be tuned by bayesian optimization. What is the best way for estimation of error, in statistical point of view? I mean, some ...
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191 views

Monte Carlo Sampling is performing better then Bayesian Optimization

So I am testing the Bayesian optimization library for determining where to sample next by quering a test function such as 2d Rosenbrock to better reconstruct that function using Gaussian Process ...
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Choosing a space function for hyperopt

I was originally doing a grid search for my parameter optimization and with 7 parameters being optimized, it would take ages. So I am choosing to use hyperopt at this point. I am however confused on ...