# Questions tagged [minimum]

A minimum is the smallest value in a set, function, variable, distribution etc.

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### Rewards in reinforcement learning for minimization problem

I am new to ML/DL/RL. I am looking to solve the classic travelling salesman problem (TSP), where the salesman has to visit all cities only once and finding the smallest path to do that (minimize ...
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### Sample size for uniform multinomial to control minimum

I'm interested in controlling the minimum for a uniform multinomial distribution. Specifically, What would be the sample size to have the following inequality regarding the minimum? Do you know of ...
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### Min, max and average value of a multiple regression line [closed]

Let's suppose that we have a theoretical MLR as followed: sqrt(number_of_divorces_per_country) = income +0.2*income^2 -years_married +frequency_conflicts^1/4 + ε with a,b and c being the coefficients....
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### How to explain local minima found between two trained Neural networks?

I have trained 2 neural networks with SGD and then I have taken a linear path between their weights. Say W_0 and W_1 are the weight matrices of network 1 and network 2, respectively. Then I compute ...
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### Cdf of minimum of two iid random variables

I am struggling with the following sentence: Using the fact that the cumulative distribution of the minimum of two i.i.d. random variables can be expressed as $1 - (1 - F(x))^2$.... Can anyone ...
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Define $e_i$ to be iid random variables drawn from an exponential distribution with parameter $\lambda=1$. $a_i$ are numerical constants. I am interested in the probability that $a_1 + e_1 < a_2 ... 1answer 63 views ### Linear regression: Why derviative = 0 is the minimum for OLS I am new in this field, but I wanna advance fast and wan't to have a complete picture of everything. I have a very simple question, but I guess I am missing something in imagining the whole picture. ... 1answer 312 views ### Boundaries on correlation coefficient given five other correlations Is there a general formula for the boundaries of a correlation coefficient given a set of other correlation coefficients? I have seen the formula for three random variables where two correlations are ... 0answers 33 views ### Relationship between expected minimum as sample size increased Suppose I have$N$random variables$X_i$,$i = 1, \dots, N$. I am interested in the quantity $$A = \mathbb E \left[\min_{i=1, \dots, N} X_i \right].$$ Now suppose I take a subset$S \subset \{1, \...
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I am looking for a review or comparison of global optimization techniques where the gradient of the function is available and utilized to speed up search, like the following: A hybrid descent method ...
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### What is the population minimizer for Huber loss

Suppose we make predictions for a continuous outcome $Y$ conditional on a vector of covariates $X$. If we use mean squared error loss (MSE), the population minimizer is $\mathbf{E}[Y \;|\; X]$. If ...
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### Drawing the smallest value from a set of distributions

I have a specific number of normal distributions $N_D$ all with their own mean $\mu$ and std $\sigma$. Now I obtain a sample from all distributions which results in a set of $N_D$ samples. What is the ...
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### How to regularize parameters across a 2D array

I'm attempting to fit a parameter (which will be a 2D array) to an array of data which corresponds to spatial locations (i.e. longitude/latitude). The parameter can vary from point to point but I want ...
I have 3 time series X1, X2, X3. I want to find the coefficient (c1, c2) that will minimize the distance between them as follow: $$MIN\sum\sqrt{(X1-(c1*X2+c2*X3))^2}$$ The constrains are: -1< ...
Let $X$ and $Y$ be iid $\sim Normal(0,1)$ Let $A=max(X,Y)$ and $B=min(X,Y)$ What are $Var(A)$ and $Var(B)$? From simulation, I get $Var(A)=Var(B)$ approximately 0.70. How do I get this ...