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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Understanding the predictive entropy search acquisition function

The entropy search acquisition function for Bayesian optimization is: $$ \alpha_{\texttt{ES}}(\mathbf{x}) \triangleq \mathbb{H}\left[p(\mathbf{x}_{\star} \mid \mathcal{D} ) \right] - \mathbb{E}_{p(y \...
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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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Learning the number of chains in an infinite hidden Markov Model [closed]

I have a model whereby the first order Markov process $\{X_n: n \in \mathbb{N}\}$ has a transition probability matrix $P$ (unknown). This process spits out $\{Y_n: n \in \mathbb{N}\}$ with emission ...
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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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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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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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226 views

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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106 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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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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131 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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57 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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59 views

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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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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Confusion between Acquisition function and Information Gain function in Bayesian Optimization

I am reading various papers that include some form of Bayesian information. So there are various acquisition function that are suitable for various applications such as follows: Expected Improvement ...
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31 views

Multi armed bandits with Thompson sampling and unknown rewards distribution

I have machine learning models that have a some possible post processing possibilities. I would like to use multi armed bandits to select the post processing that optimizes a continuous KPI. I have ...
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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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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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192 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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cross validation for hyperparameter selection: is it correct to split data to k-folds in each try differently?

I am doing hyperparameter selection with bayesian optimization. In each iteration I compute the cross validation error, which is objective to be minimized (or times -1 and will be maximized it does ...
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59 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
121 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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Is it correct to choose different indices for cross validation in each iteration of bayesian optimization?

So I have implemented my first Bayesian Optimization for random forests in R. And now my question is whether it makes sense. I have used tune.randomForest function, which is normally for grid search,...
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168 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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67 views

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 ...
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69 views

Calculating the possible number of configurations

I am wondering how did they get the $19200$ possible configurations? Like, $5^6 = 15625$, where $6$ is the number of hyper-parameters: ps: just to check I'm doing the righ thing. Is this okay? The ...
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1answer
57 views

Bayesian update vs optimization

Say I have a multivariate normal vector $$ r \sim N(\mu , \Sigma ) \Rightarrow Pr \sim N(P\mu , P'\Sigma P ) $$ and I observe that $$ Pr = Q $$ Now I can use Bayes rule to calculate the ...
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207 views

Dirac Delta Function in Bayesian Optimization

I am reading a paper on Bayesian optimization which aims at selecting the batch of points $x_0,x_1,..,x_k$ to sample to obtain maxima or minima of the GP. So the first batch element is normal ...
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How does Bayesian provide Gaussian Process the capability of against overfitting

As frequently mentioned in books and papers, Gaussian Process for Regression has a nice built-in ability to against overfitting. This can be somewhat understandable solely from the equation ...
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61 views

What is Gaussian in BO: Can I use bayesian optimization for binary classification task?

BO works based on gaussian process, so what is gaussian there? Can I use BO for binary classification task, for example neural network which has output with logistic activation and is minimizing ...
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understanding bayesian optimization: what is meant by dimension

What is meant by the dimension in bayesian optimization? In many papers it is stated that the dimension should be lower than 20 (then there are papers which are solving high-dimensional problem). But, ...