Tagged Questions
1
vote
1answer
99 views
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 ...
3
votes
0answers
83 views
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 ...
0
votes
0answers
37 views
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 ...
3
votes
0answers
61 views
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 ...
1
vote
1answer
280 views
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 ...
0
votes
1answer
78 views
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 ...
2
votes
2answers
518 views
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 ...
1
vote
1answer
87 views
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 ...
2
votes
1answer
92 views
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 ...
10
votes
3answers
971 views
Best fit ellipsoid
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 ...
3
votes
3answers
413 views
Optimally combining samples to estimate averages
Suppose I have two tables, each of unknown size, and I'd like to estimate the average of their true sizes. I hire 2 contractors: one guarantees good precision (i.e., her measurement ...
