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In <math>I = \displaystyle\int h(x)f(x)\,dx</math>, Monte Carlo simulation can be used only if it easy to sa :: <math>I = \displaystyle\int h(x)f(x)\,dx </math> ...

...I = \displaystyle\int h(x)f(x)\,dx </math> <math>= \displaystyle\int \frac{h(x)f(x)}{g(x)}g(x)\,dx</math> We continue our discussion of Importance Sampl ...s just <math> \displaystyle E_g(h(x)) \rightarrow</math>the expectation of h(x) with respect to g(x), where <math>\displaystyle \frac{f(x)}{g(x)} </math ...

<math> I = \displaystyle\int^\ h(x)f(x)\,dx </math> :: <math>= \displaystyle\int \ h(x)\frac{f(x)}{g(x)}g(x)\,dx</math> ...

:<math>I = \displaystyle\int_a^b h(x)\,dx</math> :<math>w(x) = h(x)(b-a)</math> ...

In <math>I = \displaystyle\int h(x)f(x)\,dx</math>, Monte Carlo simulation can be used only if it easy to sa :: <math>I = \displaystyle\int h(x)f(x)\,dx </math> ...

h+1 & = \dfrac{abc}{\text{def}}\\ ...th>h</math> agrees with the task-assignment ability of humans <math>\tilde h</math> on whether each observation in the data "is" or "is not" in task <ma ...

...nary codes <math>h</math> and <math>g</math> with hamming distance <math>||h-g||_H</math> and a similarity label <math>s \in {0,1}</math> the pairwise h l_{pair}(h,g,\rho)= ...

Assume <math> v \in \{0,1\}^{N_v}</math> and <math> h \in \{0,1\}^{N_h}</math> are the vectors of binary valued variables, corres P(v,h) = \frac{1}{Z} exp(v^{T}Wh+v^{T}b_{v}+h^{T}b_{h}) ...

...euristic with application to minimum order system approximation, M. Fazel, H. Hindi, and S. Body]</ref> focuses on the following problems: ...utorial.pdf Rank Minimization and Applications in System Theory, M. Fazel, H. Hindi, and S. Body]</ref>]] ...

...ath> drawn from other Dirichlet process <math>DP(\lambda, H)</math>, where H is any base measure. Note that <math>G_0</math> is discrete with probabilit <math> G_0 </math> ~ <math> DP(\lambda,H) </math> ...

<math>P(w|h)=\frac{e^{\sum_{k=1}^N \lambda_i f_i(s,w)}} {\sum_{w=1} e^{ \sum_{k=1}^N\l ...e\sum_{k=1}^N \lambda_i f_i(h,w)} {\sum_{w=1} e \sum_{k=1}^N\lambda_i f_i(h,w)}</math> ...

...egrate. Additionally, we would like to be able to compute the posterior $p(h\mid x)$ over hidden variables and, by Bayes' rule, this requires computatio ...his lower bound. Observe that, for any parametrized distribution $q_{\phi}(h\mid x)$, we have ...

...can be absorbed in the connections weights to the next layer. <math>\tilde{h}_j(\mathbf{x}) = h_1(\mathbf{x}) - h_2(\mathbf{x}) ...th>n_0</math> dimensional function <math>\tilde{h} = {[\tilde{h}_1, \tilde{h}_2, \ldots, ...

'''Proof''': Firstly, we need to establish <math>H</math> and <math>\pi</math> matrices commute. Since <math>H</math> is a centering matrix, we can write it as <math>H=I_{n}-11^{T}</math>. ...

...in both F and G simultaneously <ref name='S. S Lee'> Lee S. S and Seung S. H; “Algorithms for Non-negative Matrix Factorization”. </ref> Also, the facto ...rent value by some factor. In <ref name='S. S Lee'> Lee S. S and Seung S. H; “Algorithms for Non-negative Matrix Factorization”. </ref>, they prove tha ...

...nt to the eigenvalues of the Hessian matrix <math display="inline">\textbf{H}(f)</math> being bounded between <math display="inline">\alpha</math> and < ...y <math display="inline">H</math> iterations (where <math display="inline">H</math> is determined by <math display="inline">Q</math>). ...

...izing cursive handwriting <ref> A. Graves, S. Fernandez, M. Liwicki, H. Bunke, and J. Schmidhuber, [http://papers.nips.cc/paper/3213-unconstrai ...sis of the more complicated LSTM network that has composite <math>\mathcal{H}</math> functions instead of sigmoids and additional parameter vectors asso ...

...<math>g\,</math> reconstructs <math>x\,</math>. When <math>L\left(x,g\left(h\left(x\right)\right)\right)</math> denotes the average reconstruction error ...mathcal{J}_{AE}\left(\theta\right) = \sum_{x\in\mathcal{D}}L\left(x,g\left(h\left(x\right)\right)\right) </math> ...

...layer output matrix <math>\mathbf{H}</math> of ELM is given as: <math>{\bf H}=\left[\begin{matrix} {\bf h}({\bf x}_1)\\ ...

.../filter size to be 4*H and the number of attention heads to be H/64 (where H is the size of the hidden layer). Next, we explain the changes that have be ...which usually is harder. However, if we increase <math display="inline">\\H</math> and <math display="inline">\\E</math> together, it will result in a ...