All Questions
5
questions
0
votes
1
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90
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Randomness in the norm of sum of vectors
Let $x_1,x_2,\ldots,x_n \in \mathbb{R}^d$ be vectors and $a_1, a_2, \ldots, a_n \in \mathbb{R}$ be random iid scalars distributed by $N~(0,\sigma^2).$
Then, is it possible to lower bound the ...
1
vote
0
answers
76
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Probability of ell-1 norms of vertices of the rotated Hamming cube
Let $O$ be a $d$-dimensional rotation matrix (i.e., it has real entries and $OO^T = O^TO = I$). Let $\mathbf{x}$ be a uniformly random bitstring of length $d$, i.e., $\mathbf{x} \sim U(\{0,1\}^d)$. In ...
- 658
2
votes
0
answers
83
views
Upper bound in bayesian regression setting
Let $y_i = x_i^\top \beta + \epsilon_i$, $i=1,\ldots,n$; where $\epsilon_i$ are i.i.d. following a distribution with mean zero and unit variance, i.e., $\epsilon_i \sim P_{\epsilon_i}(0,1)$, $i=1,\...
- 81
1
vote
1
answer
609
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Find an upper bound on the expectation of squared norm given an upper bound on the expectation of norm
For non-independent random vectors $X, Y$, I have an upper bound on the expectations $E[\|X\|_2] \leq a, E[\|Y\|^2_2] \leq b$. How can I compute an upper bound for $E[\|X^\intercal Y\|_2]$ or $E[\|X^\...
- 1,180
0
votes
1
answer
43
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Mean of a function, under different distributions
Define a function: $f: X \rightarrow \mathbb{R}$. The notation $\mathbb{E}_{x \sim D}[f(x)]$ denotes the mean of the function under distribution $D$, where $D$ is a continuous distribution defined ...
- 2,670