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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 ...

variables H in addition to X, with the Markov chain state (and mixing) involving both X and H. Here H is the angle about ...

...is the <math>0^{\text{th}}</math> layer and the output layer is the <math>H^{\text{th}}</math> layer). The input <math>X</math> is a vector with <math> ...dom network output <math>Y</math> is <math>Y = q\sigma(W_H^{\top}\sigma(W_{H-1}^{\top}\dots\sigma(W_1^{\top}X)))\dots),</math> where <math>q</math> is a ...

...selects whether the hidden state is to be updated with a new hidden state h˜. The reset gate r decides whether the previous hidden state is ignored. ]] ::<math> r_j=\sigma([\mathbf{W}_r\mathbf{x}]_j+[\mathbf{U}_r\mathbf{h}_{t-1}]_j )</math> <br/> ...

The vocabulary is represented by a matrix <math> \mathbf{E}\in \mathbb{R}^{h \times v} </math> with a look up layer, denoted by the embedding <math> e_\ ...define the local context unit <math> \mathbf{K}_{\omega_i}\in \mathbb{R}^{h\times\left (2c+1\right )}</math>. Let <math> \mathbf{K}_{\omega_i,t} </math ...

...ight matrix from the projection layer to the hidden layer and the state of H would be: <math>\,h=tanh(Ha + b)</math> where A is the concatenation of all <math>\,a_i</math> ...

...ode G which passes the ball to nodes I & D. Node F passes the ball to node H which passes the ball to the already visited node, I. Therefore all nodes a H ...

...dentically distributed), <math>X</math> and associated hidden labels <math>H</math> are generated by the following model: $$P(X, H) = \prod_{i = 1}^N P(X_{i,1}, \dots , X_{i,N_i}| H_i)P(H_i) \quad \quad \ ...

...ngle af+bg,h\rangle=a\langle f,h\rangle+b\langle g,h\rangle,\,\forall\,f,g,h\in\mathcal{F}</math> and all real <math>\,\!a</math> and <math>\,\!b</math> ...f\otimes g)h:=f\langle g,h\rangle_{\mathcal{G}} \quad</math> for all <math>h\in\mathcal{G}</math> ...

<math>(f\otimes g)h:=f<g,h>_\mathcal{G}</math> for all <math>h\in \mathcal{G}</math> where <math>H,K,L\in \mathbb{R}^{m\times m},K_{ij}:=k(x_i,x_j),L_{i,j}:=l(y_i,y_j) and H_ ...

[3] H. B. McMahan. Follow-the-regularized-leader and mirror descent: Equivalence [4] T. Mikolov, A. Deoras, D. Povey, L. Burget, and J. H. Cernocky. Strategies for training large scale neural network language mode ...

The projection pursuit concept was developed by Jerome H. Friedman and John Tukey in 1974. ...x to obtain a subspace of dimension <math>k_{0}</math>. The value of <math>h</math> is chosen as ...

A valid hash function <math>h</math> must satisfy the property Pr[h(x_i)= h(x_j)] = sim(x_i, x_j) ...

<math> \hat{Q}(h(S), v;\Theta) = \theta_5^{T} relu([\theta_6 \sum_{u \in V} \mu_u^{(T)}, \th <math>r(S,v) = c(h(S'),G) - c(h(S),G);</math> ...

...\times H} </math>, where the size of the image is <math>3 \times W \times H</math> as the preturbation. In this case, <math>Dissim(\delta)=0 </math>. ...nels of a pixel are not equal and it uses <math> \delta_{3 \times W \times H} </math> with the <math>Dissim(\delta) = || \delta_{R}- \delta_{B}||_p + | ...

...\alpha)</math> is defined using two parameters. The first parameter, <math>H</math>, is a base distribution. This parameter can be considered as the mea <math>\, \theta_k</math>~<math>\, H</math> ...

...opposed to computing the inner product. Denoting the weak classifiers by $h(\cdot)$, we obtain the strong classifier as: H(x_i) = \sum\limits_{j = 1}^K \alpha_j h(x_{ij}; \lambda_j) ...

where |Ω| is the size of the data set, H_n is the nth chunklet, |H_n| is the size of the nth chunklet, and N is the number of chunkl ...ximize the entropy of Y, H(Y). This is because I(X,Y) = H(Y) – H(Y|X), and H(Y|X) is constant since the transformation is deterministic. Intuitively, si ...

a_{t} =h_{t-1}^{cat} W^h + b^h \hspace{2cm} (2) <math>W^h∈R^{(R+M)\times M} </math> guarantees each hidden state provided by the prev ...

Bilen, H., and Vedaldi, A. 2017. Universal representa- tions: The missing link betwe Rebuffi, S.-A.; Bilen, H.; and Vedaldi, A. 2017. Learning multiple visual domains with residual adap ...

..., which are then multiplied by the weight matrix <math>w_h</math> in <math>h</math> to produce the output logits as shown in Figure 1. ...

...<math>g \,</math> and <math>h \,</math>, <math>g(y_i) \,</math> and <math>h(y_j) \,</math> are uncorrelated. ...possible values <math>\{x_1, x_2, ..., x_n\} \,</math> is defined as <math>H(X) = -\sum_{i=1}^n {p(x_i) \log p(x_i)}</math> ...

...finite sequences of words in the source and target language, and let <math>H'</math> denote the set of finite sequences of vectors in the latent space. ...s a sequence of hidden states <math display="inline">(h_1,\ldots, h_m) \in H'</math> in the latent space. Crucially, because the word vectors of the tw ...

...to the largest singular value of A. Therefore, for a linear layer <math> g(h)=Wh </math>, the norm is given by <math> ||g||_{Lip}=\sigma(W) </math>. Obs ...ator more sensitive, one would hope to make the norm of <math> \bar{W_{WN}}h </math> large. For weight normalization, however, this comes at the cost of ...

...The authors define the deconfusing function as an indicator function <math>h(x, y, g_k) </math> which takes some sample <math>(x,y)</math> and determine $$ R(g,h) = \int_x \sum_{j,k} (f_j(x) - g_k(x))^2 \; h(x, f_j(x), g_k) \;p(f_j) \; p(x) \;\mathrm{d}x $$ ...

stochastic binary feature vector <math> \mathbf h </math> are modeled by products of conditional Bernoulli distributions: <br> <center> <math> \mathbf p(x_i=1|h)= \sigma(b_i+\sum_{j}W_{ij}j_j) </math> </center> ...

Let <math>({ H}_1, k_1)</math> and <math>({H}_2, k_2)</math> be RKHS over <math>(\Omega_1, { B}_1)</math> and <math>(\Om <math><f, \Sigma_{YU}g>_{{H}_1} \approx \frac{1}{n} ...

...purpose of the latent vector is to model the conditional distribution $p(x|h)$ such that we get a probability as to if the images suites this descriptio $$p(x|h) = \prod\limits_{i=1}^{n^2} p(x_i | x_1, ..., x_{i-1}, h)$$ ...

<math> E\left(\mathbf{v}, \mathbf{h}; \mathbf{W}\right) = - \sum_{i \in visible}a_iv_i - \sum_{j \in hidden}b_j * <math>\mathbf{h}</math> is the vector of hidden units, with components <math>h_j</math> and ...

:<math>PP(p) := 2^{H(p)}=2^{-\sum_x p(x)\log_2 p(x)}</math> Here <math>H(p)</math> is the entropy in bits and <math>p(x)</math> is the probability o ...

h <math>(x, y)</math> and <math>(w, h)</math> are normalized to the range <math>(0, 1)</math>. Further, <math>p_c ...