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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 ...

[1] S. Y. Xia, H. Pan, and L. Z. Jin, “Multi-class SVM method based on a non-balanced binary H. Yu and C. K. Mao, “Automatic three-way decision clustering algorithm based ...

<math> I = \displaystyle\int^\ h(x)f(x)\,dx </math> by <math>\hat{I} = \frac{1}{N}\displaystyle\sum_{i=1}^Nh ...

...n its value never changes quicker than the function <math display="inline">h(x)=Kx</math>. The reason the activation functions are Lipschitz continuous [3] Han, S., Mao, H., and Dally, W. J. Deep compression: Compressing deep neural networks with ...

...all $f \in \mathcal{H}_K$. Now, if we take $\phi: \mathcal{X} \to \mathcal{H}_K$, then we can define the MMD between two distributions $p$ and $q$ as fo ...thbf{E}_{x\sim p}(\phi(x^s)) - \mathbf{E}_{x\sim q}(\phi(x^t))||_{\mathcal{H}_K} ...

...to the subspace spanned by the columns of <math>U_d</math>. A unique <math>H^+</math> solution can be obtained by finding the pseudo inverse of <math>X< ...ath> <math>X= U \Sigma V^T</math> <math>X^+ = V \Sigma^+ U^T</math> <math>H^+= U \Sigma V^T V \Sigma^+ U^T =UU^T</math> For each rank <math>d</math>, ...

* Li, H., Kadav, A., Durdanovic, I., Samet, H., & Graf, H. P. (2016). Pruning filters for efficient convnets. arXiv preprint arXiv:16 * Han, S., Mao, H., & Dally, W. J. (2015). Deep compression: Compressing deep neural networks ...

...hbf{h}_1), (\mathbf{x}_{2k}, \mathbf{h}_2) , ... (\mathbf{x}_{nk}, \mathbf{h}_n) } ...

...\bf h}_{t-1} \in \mathbb{R}^d</math> and outputs the new state <math>{\bf h}_t </math> (although the dimensions of the hidden state and input are the ...\alpha({\bf x}_t, {\bf h}_{t-1})) = \text{softmax}({\bf W}[{\bf x}_t; {\bf h}_{t-1}]+{\bf b}) \in \mathbb{R}^k</math> ...

...^m-y_j^m ||^2, \quad z_i=\sum_{h}\sum_{m} \pi_{i}^{m} \pi_{h}^{m} e^{-d_{i,h}^{m}} </math> </center> ...

...uch that <math>\beta \leq \frac{wh}{WH}</math> and <math>\gamma \leq \frac{h}{w} \leq \gamma^{-1}</math>. The smalles size of crops is at least <math>\b ...

...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) } ...

kern(h,q) = \frac{1}{\epsilon + ||h-q||^2_2}. ...

...vectors are concatenated to form a vector <math>h</math>. The vector <math>h</math> is then projected to <math>\mu</math> and <math>\sigma</math> via t <math>\mu =W_\mu h + b\mu</math> ...

<math>a</math> is considered as a modulating factor and <math>h{(a,p)}=\frac{1}{ap+(1-a)} \in (0,1]</math> is a modulating function [1]. Th ...e because it could be larger than the softmax probability, while <math>p_m=h(a, p)*p < p </math> always holds. ...

...ResNet50x1, ResNet152x2 to the ViTs ViT-B/32, ViT-B/16, ViT-L/16, and ViT-H/14. The data used to train the models, unless specified, is the JFT-300M da * M. Naseer, K. Ranasinghe, S. Khan, M. Hayat, F. S. Khan, and M.-H. Yang. Intriguing properties of vision transformers, 2021. ...

...previous states, and the use of Echo State networks, <ref> Jaeger, H. and H. Haas. [http://www.sciencemag.org/content/304/5667/78.short "Harnassing Non ...essian of the cost function.In fact instead of computing and inverting the H matrix when updating equations, the Gauss-Newton approximation is used for ...

...e input. The classification rule used by a classifier has the form <math>\,h: \mathcal{X} \mapsto \mathcal{Y} </math>. ...mpirical error rate is the frequency where the classification rule <math>\,h</math> does not correctly classify any data input in the training set. In e ...

...n of the conformation problem formulation <ref name="bis"/> <ref>Leung N. H., and Toh K.-C. (2009) An SDP-based divide-and-conquer algorithm for large- ...d local tangent space alignment (LTSA) <ref name="zhan">Zhang, Z. and Zha, H. (2002) Principal manifolds and nonlinear dimension reduction via local tan ...

h(v_I,v_{I^t})=\frac{\exp \biggl( \frac{s(v_I,v_{I^t})}{\tau} \biggr)}{\exp \ ...{t})=-\text{log}[h(f(v_I),g(v_{I^t}))]-\sum_{I^{'}\in D_N}^{} \text{log}[1-h(g(v_{I^t}),f(v_{I^{'}}))] ...

...xtbf{P}} = [\textbf{P}^{[CLS]}_1,...,\textbf{P}^{[CLS]}_k] \in \mathbb{R}^{h \times k}</math>. Here <math> \textbf{w}_{start},\textbf{w}_{end},\textbf{w ...

<div align="center">Figure 2: Architecture of the 3-cluster APLC. h denotes the hidden state. Vh denotes the head cluster. V1 and V2 denote the [3] Jain, H., Prabhu, Y., and Varma, M. Extreme multi-label loss ...

* <math>T :=(L_T, P_T(x), P_T(x_t | x_{t-1}, a_{t-1}), H )</math> (A Task) * <math>H</math>: The horizon of the MDP. This is a fixed natural number specifying t ...

...ntly, if the the largest singular value of <math display="inline">\mathcal{H}</math> is less than 1. To find the singular values of <math display="inline">\mathcal{H}</math>, the authors used an explicit formula derived by Blinn [2] for <mat ...

...}, h_{ \leftarrow})</math> are concatenated to form a latent vector, <math>h</math>, of size <math>N_{z}</math>, &h = [h_{\rightarrow}; h_{\leftarrow}]. ...

[3] Brodersen, K. H., Ong, C. S., Stephan, K. E., and Buhmann, J. M. (2010). The balanced accur [13] Wu, Y., Charoenphakdee, N., Bao, H., Tangkaratt, V., and Sugiyama, M. (2019). Imitation learning from imperfec ...

...the translation vector of y based on the encoded sequence of hidden states h: <math>p(y_t\,|\,y_{<t},x)\propto \exp\{q(y_{t-1}, z_t, c_t)\}</math> where ...

...t one non-zero component, follow a <math>Poisson(\alpha H_N)</math>, where H_N is the ''N''th harmonic number, i.e. <math>H_N=\sum_{j=1}^N \fr ...

Let <math>h^{c}_{t-1}, h^{r}_{t-1} \in \mathbb{R}^m</math> denotes the two hidden layers where m = d : <math>h^{c}_{t-1} = f(W x_{t-1}^{c} + U h_{t-1}^{r} + b) </math> ...

$(x, y) = \displaystyle arg \min_{(x_i,y_i) \in S} d(h(x_i), h(\hat{x})) $ The function h is parameterized by Inception – one of the best performing ImageNet classif ...

...onneau, 2017]''' Conneau, A., Lample, G., Ranzato, M., Denoyer, L., Jégou, H., "Word Translation without Parallel Data". arXiv:1710.04087 ...

Dg[W](H)= H^T W + W^T H. D^\ast g[W](H)= WH^T +WH. ...

# $\bar{h} = \frac{1}{T_x}\sum\limits^{T_x}_{l=1}h_l$ # $𝜇_{CC} = f_{CC}([\bar{c_{t}},\bar{h}])$ ...

<br><math>H\left({\boldsymbol{\alpha} }\right)=\frac{1}{N}\sum^N_{n=1}{F\left({{\mathbf ...g to make the solution sparse. The learning algorithm is to minimize <math>H\left({\boldsymbol{\alpha} }\right)</math> with respect to <math>{\boldsymbo ...

H &= tanh(W_xX + (W_gg)𝟙^T)\\ a_x &= softmax(w_{hx}^T H)\\ ...

...rying k with different hidden unit sizes <math>h</math> by keeping <math>k*h</math> or a similarly related term constant. This is better studied in [5] # Speech and Language Processing. Daniel Jurafsky & James H. Martin. 2017. Draft of August 28, 2017. ...

...f dimensions h x w, a stacked hourglass (Appendix 2) is used to generate a h x w x f representation of the image. It should be noted that the dimension ...

<center><math> \frac{H}{\theta} = \frac{T}{1-\theta} </math></center> \begin{center} H = \# of all <math>x_i = 1</math>, e.g. \# of heads <br /> ...

...the model, the observed points are encoded using a three-layer MLP encoder h with a 128-dimensional output representation. The representations are aggre of the encoder h to include convolution layers as ...

...ion. We use this to solve an integral of the form: <math> I = \int_{a}^{b} h(x) dx </math> \displaystyle I & = \int_{a}^{b} h(x)dx \\ ...

Lee, H., Battle, A., Raina, R., and Ng, A.Y. Efficient Lee, H., Chaitanya, E., and Ng, A. Y. Sparse deep belief ...

...minimize here during training is <math>E=-\sum_a\sum_{k=1}^{C}{y_{n,k}log(h{n,k})}</math>, where <math>n</math> denotes the training example, and <math ...

...ion problem is generally NP-hard<ref name="fazel2004">Fazel, M. and Hindi, H. and Boyd, S. Rank minimization and applications in system theory. Proceedi ...ine Learning Research'', 7:2541-2563, 2006.</ref> and Zou<ref name="Z2006">H. Zou. The adaptive lasso and its oracle properties. ''Journal of the Amer ...

[2] Y. Song, J. Huang, D. Zhou, H. Zha, and C. L. Giles, “IKNN: Informative K-nearest neighbor pattern classi [12] Z. H. Zhou and Y. Yu, “Ensembling local learners throughmultimodal perturbation, ...

3. Dulac-Arnold, G.; Evans, R.; van Hasselt, H.; Sunehag, P.; Lillicrap, T.; Hunt, J.; Mann, T.; Weber, T.; Degris, T.; an 6. VanHasselt,H.,andWiering,M.A. 2009. Usingcontinuousactionspacestosolvediscreteproblems. ...

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

...e distributed data fusion technique, Channel Filter <ref> A. Makarenko and H. Durrant-Whyte, “Decentralized Bayesian algorithms for active sensor networ ...

Use the cluster membership <math>H=(h_i^k) </math> obtained to reconstruct the K centres <math>C_{\mu}^* = [ \ ...

...y but all three have the same fundamental idea. This is given by <math>2^{{H(p)}}=2^{{-\sum _{x}p(x)\log _{2}p(x)}} </math> Suppose you have a four-side ...of input elements. The output of l-th block of decoder is denoted by <math>h^l = (h_1^l,....,h_n^l)</math> and <math>z^l = (z_1^l,....,z_m^l)</math>. Ea ...

\min_{u \in \mathbb{R}^n} \max_{v \in \mathbb{R}^m} \ u^T P v -H(v) + H(u) \\ where H(y) is the Gibbs entropy <math> \sum_i y_i log y_i</math>. ...

To avoid overfitting, the authors add causal entropy <math>−H (\pi_{\theta}) </math> as the regularization term. Thus, the learning objec \[\min_{\theta}\mathcal{L}=-\eta(\pi_{\theta})-\lambda_{2}H(\pi_{\theta})+\lambda_{1} \sup_{{D\in(0,1)}^{S\times A}} \mathbb{E}_{\pi_{\ ...

...h or horizon of a demonstration, and some evaluation function $$R_t(d): R^H \rightarrow R$$ are given, and that succesful demonstrations are available ...

[1] S. Wang, R. Clark, H. Wen and N. Trigoni, "DeepVO: Towards end-to-end visual odometry with deep [15] R. Roberts, H. Nguyen, N. Krishnamurthi, and T. Balch, “Memory-based learning for visual ...

with Hilbert-Schmidt norms. In S. Jain, H. U. Simon, and E. Tomita, editors, Proceedings ...esented above. ii) The kernel matrices have to become centered via matrix H. <br> ...

...roduced by I to an individual memory slot, and just updates the memory at $H(I(x))$. # Li, Jiwei; Miller, Alexander H.; Chopra, Sumit; Ranzato, Marc'Aurelio; Weston, Jason. "Dialogue Learning W ...

...\cdot)dP_z(z) - \int_{{\mathcal{Z}}} k(z,\cdot)dQ_z(z) \parallel_{\mathcal{H}_k}, where <math>\mathcal{H}_k</math> is the reproducing kernel Hilbert space of real-valued functions ...

# Z. Akata, S. Reed, S. Mohan, S. Tenka, B. Schiele, H.Lee. Learning What and Where to Draw. In NIPS 2016 # Z. Akata, S. Reed, D. Walter, H. Lee, and B. Schiele. Evaluation of Output Embeddings for Fine-Grained Imag ...

A.W. Black, H. Zen, and K. Tokuda, “Statistical parametric speech synthesis,” in Proc. IC ...

...\sqrt{\lambda/2\pi e^{-C(\omega;M)}} </math>, where <math>C(\omega;M) = H(\omega;M) + \lambda\omega^2/2 </math> denotes the L2 regularized cross en #Richard H Byrd, Gillian M Chin, Jorge Nocedal, and Yuchen Wu. Sample size selection i ...

To recall, Hadamard matrix (Hedayat et al., 1978) <math> H </math> is an <math> n × n </math> matrix, where all of its entries are eit ...he entire Hadamard matrix <math>H</math>, a truncated version, <math> \hat{H} &isin; </math> {<math> {-1, 1}</math>}<math>^{C \times N}</math> where all ...

# Construct <math>H</math> be a perfect hash function with <math>L</math> buckets, and <math>\p # <math>*</math>Construct <math>\phi(z_i, z_{i,j}, z_j) = \mathbf{1}[H(z_j)] z_{i,j}</math>, which intuitively means that <math>\phi</math> stores ...

11. J. Dai, H. Qi, Y. Xiong, Y. Li, G. Zhang, H. Hu, and Y. Wei. Deformable convolutional networks. In ICCV, 2017. ...

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>\, ...

O. Abdel-Hamid, A. Mohamed, H. Jiang, and G. Penn, “Applying convolutional ...

...hbb{E}_{\pi}[log(D(s,a)]\ +\ \mathbb{E}_{\pi_E}[log(1 - D(s,a))] - \lambda H(\pi)) where <math> H(\pi) \triangleq \mathbb{E}_{\pi}[-log\: \pi(a|s)]</math> is the entropy. ...

...a. Readers are referred to the book "Introduction to algorithms" by Thomas H. Cormen for the formal definition of Schur complement and the proof of the ...

...., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). [http://arxiv.org/pdf/1406.1078.pdf Learning phrase ...

...el, x is a w×h image, z_k is a feature map of dimension (w+s-1)×(h+s-1), and * denotes the discrete convolution operator. ...

...y "Segmentation, minimum spanning tree and hierarchies."] In L. Najman and H. Talbot, editors, Mathematical Morphology: from theory to application, chap ...

...we encode symbols from <math>y</math> using the wrong tool <math> {\hat h}</math> . This consists of encoding the <math> {i_{th}}</math> symbol using H(y,\hat y) = \sum_i{y_i\log{\frac{1}{\hat y_i}}} ...

...4) <ref>Cho, K., van Merrienboer, B., Gulcehre, C., Bougares, F., Schwenk, H., and Bengio, Y. (2014a). ...

# Reed, S. E., Akata, Z., Mohan, S., Tenka, S., Schiele, B., & Lee, H. (2016). Learning what and where to draw. In Advances in Neural Information # Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., ... & Berg, A. C. (2015). Imagenet larg ...

...(s_t))\bigtriangledown_\theta log\pi(a_t|s_t)+\beta\bigtriangledown_\theta H(\pi(.|s_t))</math> ...factor <math>0 < \gamma \leq 1, \alpha</math> is the learning rate, <math>H (·)</math> is an entropy regularizer, and <math>\beta</math> is the regular ...

...The Multiplicative Congruential Method, invented by Berkeley professor D. H. Lehmer, may also refer to the special case where <math>b=0</math> and the Take h(x) = f(x)/g(x) and solve for h'(x) = 0 to find x so that h(x) is maximum. ...

...(z)} - \int \limits_{\mathcal{Z}} {k(z, \cdot)dQ_Z(z)} \right \|_{\mathcal{H}_k} where <math>\mathcal{H}_k</math> is the RKHS (reproducing kernel Hilbert space) of real-valued fun ...

...T is first applied on the rows and then the columns. If a low (L) and high(H) sub-band is extracted from the rows and similarly for the columns than at ...

...ions (h,w,c), i.e. height, width, and # of channels, and the output being (h’, w’, k), i.e. output height, width, and # of filters, we know that the the ...tion ''h'' mapps the keys to an element from the set {1...M} -- i.e. <math>h(k) &isin; {1...M}</math>, <math>&forall; k &isin; U</math>. This allows for ...

.... PAMI'', vol.31, no. 2, pp. 210-227, 2009.</ref><ref>R. Raina, A. Battle, H. Lee, B. Packer, and A. Y. Ng. Self-taught learning: transfer learning from ...

[2] S. Reed, H. Lee, D. Anguelov, C. Szegedy, D. Erhan, and A. Rabinovich. Training deep n ...

...tor in the <math>\,(N-M)</math> dimensional translated null space <math>\,H=N(\theta)+s</math>. Related to the concept of [http://en.wikipedia.org/wiki ...

In classification,, we attempt to approximate a function <math>\,h</math>, by using a training data set, which will then be able to accurately ...e set of labels, We try to determine a ''''classification rule'''' <math>\,h</math> such that, ...

l_{smoothness}(\mathbf{u}, \mathbf{v}) = \sum\limits_j^H\sum\limits_i^W \Big(\rho_S(u_{i,j}, u_{i+1, j}) + \rho_S(u_{i,j} - u_{i, j+ ...

[1] Ince, H., Trafalis, T.B., "Kernel principal component analysis and support vector m H. White, “Learning in artificial neural networks: A statistical ...

[6] Bussell E. H., Dangerfield C. E., Gilligan C. A. and Cunniffe N. J. 2019Applying optimal ...

...ality from the space X to the dimensionality of space Y by passing through H without having to know '''<math>\Phi(X)</math>''' exactly. :<math>K = -\frac{1}{2}HD^{(X)}H</math> ...

The ultimate goal of multiclass classification is to learn a mapping <math>\,H : \mathcal{X} \mapsto \mathcal{Y}</math> from instances in <math>\,\mathcal ...

...epeated Loss Minimization]" by Hashimoto, T. B., Srivastava, M., Namkoong, H., & Liang, P. which was published at the International Conference of Machin ...

...Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, C¸ aglar Gulc¸ehre, H. Francis Song, Andrew J. Ballard, Justin Gilmer, George E. Dahl, Ashish ¨ V ...

1 &\quad \text{if } \hat{r}_t > q^{h}_t\\ ...

# Teerapittayanon, Surat, Bradley McDanel, and H. T. Kung. "Branchynet: Fast inference via early exiting from deep neural ne ...

[4] W Falcon, H Schulzrinne, Predicting Floor-Level for 911 Calls with Neural Networks and ...

...optimization problem can be written as:<center> <math> \min_{f\in\mathcal{H}_{\otimes}} R_{N}(f)+\lambda\parallel f \parallel^2_\otimes </math> </cente ...

...hen <math>\alpha \in [-1,1]</math> and <math>\beta \in [0,1]</math>. Cases H and F outperform PyramidNet, suggesting that the strong perturbations impos ...

The '''true error rate''' for classifier <math>h</math> is the error with respect to the unknown underlying distribution whe <math>L(h) = P(h(X) \neq Y )</math> ...

.../math> denote the input, forget, and output gate, <math display = "inline">h</math> is the hidden state and <math display = "inline">c</math> is the cel ...

...h>\,W_{oh}</math> is the hidden to output weight matrix. Vector <math>\,b_{h}</math> and <math>\,b_{o}</math> are the biases. When t=1, the undefined <m ...

...h>\,W_{oh}</math> is the hidden to output weight matrix. Vector <math>\,b_{h}</math> and <math>\,b_{o}</math> are the biases. When t=1, the undefined <m ...

...h>\,W_{oh}</math> is the hidden to output weight matrix. Vector <math>\,b_{h}</math> and <math>\,b_{o}</math> are the biases. When t=1, the undefined <m ...

An LDPC code is a block code that has a sparse parity check matrix <math>\ H </math>. The parity check matrix of an LDPC code can be represented by a bi ...

...ion into the human representation and processing of visual information. W. H. Freeman and Company, 1982. ...

...hat intrinsically difficult; it just seems so when we do it." <ref>Moravec H. (1988). Mind Children: The future of robot and human intelligence. Massach ...

\psi_{c_i} (x_{c_i}) = exp (- H(x_i)) P(x_{V}) = \frac{1}{Z} \prod_{c_i \epsilon C} exp(-H(x_i)) = \frac{1}{Z} exp (- \sum_{c_i} {H_{c_i} (x_i)}) ...

# Han, S., Mao, H., & Dally, W. J. (2015). Deep compression: Compressing deep neural networks ...

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[6] Kuo, H. "Introduction to Stochastic Integration Springer." Berlin Heidelberg (2006 ...

Hasselt, H. V., et al. [http://arxiv.org/pdf/1509.06461.pdf " Deep reinforcement learn ...

...hose feature values is <math>\,x</math> is given the label <math>\,\hat{Y}=h(x)</math>. ...r training data, we could use the classifier's classification rule <math>\ h </math> to classify any newly-given vegetable or fruit such as the one show ...

H. Zhou, J. M. Alvarez, and F. Porikli. Less is more: Towards compact CNNs. I ...

[1] Shankar, V., Roelofs, R., Mania, H., Fang, A., Recht, B., & Schmidt, L. (2020). Evaluating Machine Accuracy on ...

E_1^D = BiLSTM_1(L^D) \in R^{(h×(m+1))} E_1^Q = tanh(W BiLSTM_1(L^Q) \in R^{(h×(n+1))} ...

#Richard H Byrd, Gillian M Chin, Jorge Nocedal, and Yuchen Wu. Sample size selection i ...

[15] Jospin, L. V., Buntine, W. V., Boussaid, F. V., Laga, H. V., & Bennamoun, M. V. (2020). Hands-on Bayesian Neural Networks - a Tutor ...

[3] Albert Bandura and Richard H Walters. Social learning theory, volume 1. Prentice-hall Englewood ...

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[9] Heaton, J. B., Polson, N. G., and Witte, J. H. Deep learning in finance, February 2016. ...

2. Papadimitriou, Christos H., Mihalis Yannakakis. Structure in Complexity Theory Conference. IEEE. May ...

[4] L. Castrejon, Y. Aytar, C. Vondrick, H. Pirsiavash, and A. Torralba. Learning aligned cross-modal representations ...

...d by parameter vector $\theta$, $$\displaystyle \max_{\Theta}E[\sum_{t=0}^{H}R(s_{t})|\pi_{\theta}]$$ $\pi_{\theta}(u|s)$ is the probability of action u ...

# Yamamoto, M., Kato, S., and Iizuka, H. Digital curling strategy based on game tree search. In Proceedings of the ...

[13] M. T. Dzindolet, S. A. Peterson, R. A. Pomranky, L. G. Pierce, and H. P. Beck. The role of trust in automation reliance. Int. J. Hum.-Comput. St ...