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...oth mappings of labelled and unlabelled images by <math>g</math> and <math>h</math> respectively will be utilized. ...tion loss <math>\mathcal{L}_{ss}</math> utilizes a separate function <math>h</math> which maps the embeddings of unlabeled images to a separate label sp ...

where x's are the feature values of each data point, and h's are the weights of the corresponding x's. <math>r_k(z) = \frac{1}{\sum_{(x,h) \in D_k} h} \sum_{(x,h) \in D_k, x<z} h,</math> ...

...</math> equal to the prediction on the corresponding clean example <math> h(x) </math>. ...h>x</math> is a perturbed image <math>x'</math>, such that <math>h(x) \neq h(x')</math> and <math>d(x, x') \leq \rho</math> for some dissimilarity func ...

...{x})}}[E(\mathbf{x})]- E_{\mathbf{x} \sim q(\mathbf{x})}[E(\mathbf{x})] + H(q) ...lity was used to obtain the variational lower bound on the NLL given <math>H(q) </math>. This bound is tight if <math> q(x) \propto e^{-E(\mathbf{x})} \ ...

...h>-dimensional vector <math> \boldsymbol{c} = \left[ c_1, c_2, \dots, c_{n-h+1} \right] </math>, called a ''feature map''. ...et, we set all the hyperparameters: rectified linear units, filter windows(h) of 3, 4, 5 with 100 feature maps each, dropout rate (p) of 0.5, l2 constr ...

...h> \mathcal{U} \in \mathbb{R}^{n_{h} x n_{x} x T} </math>, where <math> n_{h} </math> is the number of hidden units and <math> n_{x} </math> is the size ...multiplication of three terms: <math>\boldsymbol W_{a} \in \mathbb{R}^{n_{h}xn_{f}}, \boldsymbol W_{b} \in \mathbb{R}^{n_{f} x T}, </math>and <math> \b ...

...on distribution $q(\mathbf{x}_{t+1}|\mathbf{x}_t)$, and an episode length $H$. In i.i.d. supervised learning problems, the length $H =1$. The model may generate samples of length $H$ by choosing an output at at each time $t$. The cost $\mathcal{L}$ provides ...

...low, L, frequency components. The assumption is that high frequency band, H, is conditionally independent of the lower frequency bands, given the middl P(H|M,L) = P(H|M) ...

...th> n </math> and the output value of the hidden layer of the model, <math>h</math>. The idea of this method is to represent the output classes as the l ...\frac{\partial Err}{\partial v_{n_i}^{'}h} \cdot \frac{\partial v_{n_i}^{'}h }{\partial v_{n_i}^{'}} </math> <br></div> ...

...set of transformations through hidden states (a.k.a layers) <math>\mathbf{h}</math>, given by the equation ...le="text-align:center;"><math> \mathbf{h}_{t+1} = \mathbf{h}_t + f(\mathbf{h}_t,\theta_t) </math> (1) </div> ...

Manager and Worker are recurrent networks (<math>{h^M}</math> and <math>{h^W}</math> being their internal states). <math>\phi</math> is a linear trans ...ed by the following equations: <math>\hat{h}_t^{t\%r},g_t = LSTM(s_t, \hat{h}_{t-1}^{t\%r};\theta^{LSTM})</math> where % denotes the modulo operation an ...

To create a common embedding, every image is represented by a set of h-dimensional vectors <math> \{v_i | i = 1 ... 20\}</math> where each <math ...fully connected layer. The matrix <math> W_m </math> has dimension <math> h \times 4096</math>. ...

[12] J. H. Friedman. Greedy function approximation: a gradient boosting machine. Anna [13] J. H. Friedman. Stochastic gradient boosting. Computational Statistics & Data An ...

Bengio, Y., Lamblin, P., Popovici, D., & Larochelle, H. (2007). Greedy layerwise Larochelle, H., Erhan, D., Courville, A., Bergstra, J., & Bengio, Y. (2007). ...

...y each encoder model is then concatenated into a single hidden state <math>h</math>. ...ightarrow(S), h_\leftarrow = \text{encode}_\leftarrow(S_{\text{reverse}}), h=[h_\rightarrow; h_\leftarrow] ...

...problem, let <math>\mathbf M_S=\mathbf {HH^T}</math> and <math>\mathbf {Q=H^TW}</math>, we get:<br> ...n Q-((H^T)^{-1}Q)^T M_D (H^T)^{-1}Q)=\min_W Trace(Q^T I_n Q-Q^TH^{-1} M_D (H^{-1})^T Q)}</math><br> ...

...math>C</math> dimensional representation, where <math>w </math> and <math>h </math> are the spatial dimensions of <math>x </math>, and the number of ch <math>H(q)</math>. <math>H(q)</math> is the entropy of the probability distribution over the symbols a ...

...> x_T^j </math>, which outputs the embedding vector <math> \overrightarrow{h^t_j} </math>, of size <math> d </math> for each bin <math> t </math> ...h> x_1^j </math>, which outputs the embedding vector <math> \overleftarrow{h^j_t} </math>, of size <math> d </math> for each bin <math> t </math> ...

...= \frac{1}{\sum_{(x,h) \in D_k} h} \displaystyle\sum_{(x,h) \in D_k, x<z} h,</math> [7] T. Chen, H. Li, Q. Yang, and Y. Yu. General functional matrix factorization using grad ...

filter(z, \delta) [i,j] = \frac{z[i,j]}{freq(w,h) [i,j]^\delta} mask(\lambda , g)[i,j] = \chi_{ top(\lambda w h, g g) } ...