Tagged Questions

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Which Queue to Join at the Super Market

Last night I started wonder about the fastest way to take a shopping trip with my university flat mates and was wonder about how we should queue for the check out. I have a feeling that queue theory ...
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Decreasing step size in SA algorithms

I don't understand why deceasing step sizes implies "implicit" averaging of the noise in stochastic approximation algorithms
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Calculating the maximum of a function

How can one determine $$\max_{f_0,f_1}\frac{\int_{\mathbb{R}}f_1(y)^xf_0(y)^{1-x}\log\left(\frac{f_1(y)}{f_0(y)}\right)\mbox{d}y}{\int_{\mathbb{R}}f_1(y)^xf_0(y)^{1-x}\mbox{d}y}$$ given ...
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Estimating the maximum of a Brownian motion over the unit interval

Let $\left(B_t\right)_{t \in \left[0,\infty\right)}$ be a standard Brownian motion over the probability space $\left(\Omega, \mathcal{A}, P\right)$. For each $x \in \left(0, \infty\right)$, give an ...
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Randomized optimization: confidence bounds

I am not sure whether the question is appropriate for MSE, so please feel free advise another website in the network. Suppose I have a Lipschitz continuous function $f:X\to \Bbb R$ where $X$ is a ...
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Bounded logarithmic function

I am trying to find any function that it grows logarithmically up to a certain point, and after that point it remains constant. Can anyone help me with that
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Theory of Moments: Notation

I try to read some papers about Moment Matrices/Optimization over polynomials, but I have some troubles with the following notation: Let $P(V)$ be a power set of some $V=\{1,2,...,n\}$, how does a ...
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Learn about reproducing kernel Hilbert spaces?

Why are reproducing kernel Hilbert spaces an important topic to learn? What is possibly achievable with that theory that is not reachable with just standard Hilbert space theory?
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Goofy problem: Optimal bet with nearly no knowledge

A year or so back, on the verge of falling asleep, I thought up this question: You have come to me ready to gamble. I have two envelopes on the table, one containing the amount of my bet, and one ...
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Relation between maximizer's derivative and maximizing function

Let $u(x)$ be a continous bounded function such that $u'(x) >0$, $u''(x) < 0$. Define $A(x) = -\frac{u''(x)}{u'(x)}>0$. Let $Y$ be a random variable with $\mathbb{E}|Y|<\infty$. I solve a ...
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How to go about optimizing this function? (Maximizing)

If we are given a fixed integer $N > 0$ of choices we can pick out of a pool of $k$ values $c_0, \cdots, c_k$ (with repetitions allowed and $c_i > 0 \forall i$) and we want to maximize the ...
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Existence of a general-purpose (almost) universal optimization strategy

From Wikipedia about interpretations of no free lunch theorem A conventional, but not entirely accurate, interpretation of the NFL results is that "a general-purpose universal optimization ...
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Understanding no free lunch theorem

From Wikipedia: $Y^X$ is the set of all objective functions $f$:$X$→$Y$, where $X$ is a finite solution space and $Y$ is a finite poset. The set of all permutations of $X$ is $J$. A random ...
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Suitable Loss function for Order preserving Factoring of a matrix?

(Old-Question) Given a $n\times n$ symmetric matrix $X$, I would like to factor it using a vector $c$ of size $n \times 1$ such that: $\sum_{i,j} [X_{ij} \cdot c_i\cdot c_j]$ is minimum. How can I ...
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One vs multiple servers - problem

Consider the following problem: We have a simple queueing system with $\lambda%$ - probabilistic intensity of queries per some predefined time interval. Now, we can arrange the system as a single ...
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What is the maximum value of the minimum number of balls per bin?

$S$ people, $N$ bins, each person has a given subset of bins he can cover, each person is given $t$ balls. Question: What is the maximum value of the minimum number of balls per bin? i.e., allocate ...
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An optimal regression problem/proof

I want to find a function $f$ that given $x$ will predict $y$. The expected prediction error of $f$ is $$e = E[(Y-f(X))^2]=\int \int [y-f(x)]^2 p(x,y) dx dy$$ the expectation of $(Y-f(X))^2$ with ...
Given a collection of points $P \subset \mathbb R^3$, a crude characterization of the "shape" of $P$ is sometimes given by the principal components. We construct a covariance matrix, e.g., if $P$ is ...