# Questions tagged [optimization]

Use this tag for any use of optimization within statistics.

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### Obtaining parameter errors with the basinhoppin method in Python

I use the basinhoppin method use in Python for global optimization. The result is named FittedParameters and is shown below: ...
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### Cranking up my validation score

My way of building a model on the MNIST dataset was to first overfit it, find a good learning scheme and then try to regularize this model to reduce the overfitting. To reduce the overfitting I'm ...
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### Constrained optimization with piecewise objective function

Here's the issue. Let's say that I have a set of inputs theta, that must satisfy some set of linear constraints such that $ui * theta - ci >= 0$ (Which is nothing more than the classical linear ...
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### Likelihood surface plotting in MATLAB [closed]

I need to find $\delta_v$ and $\delta_h$ through MLE of the Likekiood function 'f(...)' of two parameters, defined as (other than $\delta_v$ and $\delta_h$ all all known variables) where How to get ...
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### Optimal decisions based on frequentist estimators

Consider a decision problem aimed at minimizing the expected loss1 where the argument is a parameter estimate. In a Bayesian setting, given a posterior distribution of the parameter and the loss ...
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### Does EM algorithm require us to know the joint (predictive) distribution of the latent variables $Z$ when $Z$ is two-dimensional?

In its general form the E-step of the EM algorithm finds the expectation $$Q(\theta|\theta') =\int \log[ p(Y,Z | \theta)] p(Z|Y,\theta') d Z$$ where $Y$ the data, $Z$ the latent variables, $\theta'$...
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### Optimisation problem with strange side conditions

I'm dealing with the following optimisation problem: $$\min_{a \in H,\ b \in \mathbb{R}} F(a,b),$$ where $H$ is the solution space of another optimisation problem ($a$ is a real vector). I suppose as ...
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### Estimate probabilites of a sum of independant binomial (with sizes fixed)

I collect observations which are sum of K (known parameter) independant binomial variables with known number of trials but unknown probability of success: The number of trials varies for each ...
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### Optimal selection with multiple parameters

I have a problem of optimal selection given many parameters. I will try to simplify my problem in this example below: Suppose I have a basket with 100 balls in 10 different colors (not equally ...
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### Is optimizing an embedding a convex or non-convex process?

Suppose we have input data with several thousand one-hot dimensions per element, representing, say, words in a passage of text. An embedding layer is a common feature at the top of machine learning ...
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### Is penalized logistic regression convex? [duplicate]

Is logistic regression problem penalized by elastic net penalty convex optimization problem? More specifically, I want to find out whether it is suitable for dual formulation such that the duality gap ...
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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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### How to minimize the sum of Frobenius norm and Nuclear norm

I have to minimize an objective function of the the form : $||X_{s} - Y_{s}D_{s}||_{F}^{2} + ||D_{s}||_{F}^{2} + ||D_{s}||_{*}^{2}$ where $||.||_{F}$ denotes the Frobenius norm and $||.||_{*}$ ...
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### What exactly is meant by bias in this context?

I'm working through an example of survival-time analysis with censored and un-censored data. We're given the survival times of 94 patients. Some of these survival times are censored i.e.in this ...