All Questions
Tagged with machine-learning probability-distributions
8
questions
2
votes
1
answer
110
views
expectation of the product of Gaussian kernels and their input
I was wondering if anybody knows how to solve: $$\mathbb{E}{\mathbf{z} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})}\left[ (\mathbf{x}{i} - \mathbf{z})(\mathbf{x}{j} - \mathbf{z})^\top \exp\left( - (\...
- 245
2
votes
0
answers
109
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Equivalence of score function expressions in SDE-based generative modeling
I am studying the paper "Score-Based Generative Modeling through Stochastic Differential Equations" (arXiv:2011.13456) by Yang et al. The authors use the following loss function (Equation 7 ...
- 43
1
vote
1
answer
221
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Using Hoeffding inequality for risk / loss function
I've got a question to the Hoeffding Inequality which states, that for data points $X_1, \dots, X_n \in X$, which are i.i.d. according to a probability measure $P$ on $X$, we find an upper bound for:
$...
- 13
7
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2
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2k
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Mathematics of GANs (generative adversarial networks)
Generative Adversarial Networks were introduced in http://papers.nips.cc/paper/5423-generative-adversarial-nets and has more than 20000 citations.
The paper introduced key paradigm changes which ...
- 13.8k
0
votes
1
answer
3k
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In linear regression, we have 0 training error if data dimension is high, but are there similar results for other supervised learning problems?
I tried posting this question on Cross Validated (the stack exchange for statistics) but didn't get an answer, so posting here:
Let's consider a supervised learning problem where $\{(x_1,y_1) \dots (...
- 1,417
2
votes
0
answers
49
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What are some beginner's references on algebraically structured (statistical) models, and their connection with group actions and Fourier transform?
I asked this question on Cross Validated a few days ago, but didn't really get a favorable response, so asking here to see if I get any.
I'm looking at the description of a short-term position in ...
- 223
4
votes
0
answers
149
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Can we show equivalence of two distributions based on their statistics?
Let $p,q$ be two distributions on $\mathbb{R}^d$. Let $f:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}$. Under what conditions does $\mathbb{E}_{x\sim p}f(x,z)=\mathbb{E}_{x\sim q}f(x,z)\ \...
- 57
0
votes
1
answer
82
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a probability density algorithm that is not sensitive to the initial condition
There are many algorithms to estimate the density of probability distributions. I am looking for one that is not sensitive to the initial condition. For instance, Expectation–maximization algorithm ...
- 504