sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Therefore, it is very suitable for real-world sparse data.
Sentence 2: the term η u 0 is the intensity of original tweets by a user u on his own initiative, becoming the source of a cascade and the term β s v∈Fu(t) κ ω (t) ⋆ (A uv (t) dN vs (t)) models the propagation of peer influence over the network, where the triggering kernel κ ω1 (t) models the decay of peer influence over time.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (better viewed electronically with zooming) formation, our algorithm produces a better sharp estimate of the Sculpture image from [13], with fewer ringing artifacts and higher resolution details.
Sentence 2: eventually the penalty can even approach the 0 norm (although images are generally not exactly sparse, and other noise factors and unmodeled artifacts are usually present such that λ will never go all the way to zero).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For instance, in the case of regularized risk minimization we have where L is a convex function in w•x i , such as 1 2 (y i −w•x i ) 2 for regression or log[1+exp(−y i w•x i )] for binary classification.
Sentence 2: from this, Corollary 2 establishes T . This means that for a suitable choice of η we achieve exponentially fast convergence in T to some stationary distribution D * η .
Relationship: neutral
Domain: NeurIPS
Sentence 1: It should be noted that this is the first method to allow users to specify weights rather arbitrarily for all possible lenghts of matching sequences and still be able to compute kernels at O(lxl + Ix' l) time, plus, to predict on new sequences at O(l xl ) time, once the set of support vectors is established.
Sentence 2: hence, can rewrite (5) as s Eprefix (tl s Eprefix(floor(tl l i= 1 floor(t l l+l where u = floor(t), t = uv and s E prefix(v).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For model 1 the newly joined interval inherits the parameters with equal probability from the interval before or after the removed change point.
Sentence 2: if we consider the ratio of signal to noise ratios in the two states, we obtain a quantity which is independent of the fluorescence units, namely This relationship is not enforced in our model, but, if the simple birth-death interpretation is supported by the data, it should emerge naturally in the posterior distributions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Side-chain to backbone interaction seems to be much severe than side-chain to sidechain interactionthe backbone is more rigid than side-chains and its structure assumed to be known.
Sentence 2: in problems where exact inference was possible max-product BP always found the global minimum of the energy function and in the full protein data set, max-product BP always found a lower energy configuration compared to the other algorithms tested.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper we provided a step towards answering an open problem: Is parallel machine learning possible in polylogarithmic time using a polynomial number of processors only?
Sentence 2: to obtain polylogarithmic runtime of R compared to T L (M ), we choose the parameter h ≈ ld M − ld ld M such that n ≈ M /2 h = ld M . the runtime of the Radon machine is in O ld κ M + r 3 ld M . This result is formally summarised in Theorem 4.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As the regressand at step 3, we use the deviation of the impression at iteration i from the baseline impression, i.e., α i − α 0 .
Sentence 2: further, if a training pool of subjects is used to constrain model parameters (e.g., to set β or to establish priors on β and α), it's conceivable that decontamination will work without requiring much more than a single rating per item.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Most generalization studies on SGM consider the case where only one pass over the data is allowed and the step-size is appropriately chosen, [5,14,29,26,9,16] (possibly considering averaging [18]).
Sentence 2: while processing each data point only once is natural in streaming/online scenarios, in practice SGM is often used as a tool for processing large data-sets and multiple passes over the data are typically considered.
Relationship: neutral
Domain: NeurIPS
Sentence 1: More precisely, we show that for any Lebesgue-integrable 1 function f : R d → R, for any ǫ > 0, there exists a ResNet R with ReLU activation and one neuron per hidden layer such that This result implies that, compared to fully connected networks, the identity mapping of ResNet indeed adds representational power for tall networks.
Sentence 2: some regions outside the grid cells are also raised, but were supposed to be zero.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In most cases, however, our algorithm significantly outperformed the other methods.
Sentence 2: using the estimated Dirichlet parameters, the normality score of an image x is: Since all αi are constant w.r.t x, we can ignore the first two terms in the parenthesis and redefine a simplified normality score, which is equivalent in its normality ordering: As demonstrated in our experiments, this score tightly captures normality in the sense that for two images x 1 and x 2 , n S (x 1 ) > n S (x 2 ) tend to imply that x 1 is "more normal" than x 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: That is, for neurons with general non-montonic activation functions, or for neurons with monotonic activation functions whose output magnitude violates the aforementioned bounds, there are example networks that can efficiently compute any real-valued function.
Sentence 2: if an RBN network of size m can compute a real-valued function g which represents f with margin δ, then there exists a thresholded RBM network that computes f with margin δ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We first employ a simulated example to illustrate the effectiveness of the proposed sparse RIR model for BCI.
Sentence 2: in matrix-vector form, the optimization can be written as where X i is the (N + L − 1) × L convolution Toeplitz matrix whose first row and first column are [x i (k − N + 1), 0, . . . , 0] and [x i (k − N + 1), x i (k − N + 2), ..., x i (k), 0, . . . , 0] T , respectively, N is the microphone signal length, L is the filter length, h i (i = 1, 2) are L × 1 vectors representing the filters, • denotes l 2 -norm, and the constraint is to avoid the trivial zero solution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Dirichlet-multinomial conjugacy allows Φ and Θ to be marginalized out [9], while typical values for the remaining unobserved variables can be sampled from their joint posterior distribution using Markov chain Monte Carlo methods.
Sentence 2: we defined four network statistics (i.e., four discrepancy functions) that summarize meaningful aspects of the NHC network: generalized graph transitivity, the dyad intensity distribution, the vertex degree distribution, and the geodesic distance distribution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We describe how to use the shadow Dirichlet to model a random pmf that has bounded variation such that |θ k − θ l | ≤ k,l for any k, ∈ {1, 2, . . . , d} and k,l > 0.
Sentence 2: we also compared with treating all six months of sales data as coming from one multinomial which we estimated as the maximum likelihood multinomial, and to taking the mean of the six empirical pmfs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 12b tells us that, because of our assumptions about linear dimension, the matrix Σ T ,H has factors R ∈ R |T |×n and Σ S,H ∈ R n× .
Sentence 2: we also need a matrix U such that U T Φ T R is invertible; with probability 1 a random matrix satisfies this condition, but as we will see below, there are reasons to choose U via SVD of a scaled version of Σ T ,H as described in Sec.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The experimental evaluation show that our (model independent) algorithm performs as well as the Maximum Likelihood Estimator of the BTL model and outperforms other known competitors included the recently proposed algorithm by Ammar and Shah [1].
Sentence 2: their algorithm requires information about comparisons between all pairs, and for each pair it requires the exact pairwise comparison 'marginal' with respect to the underlying distribution over permutations.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (It holds when the number of rounds that a bidder can participate in is at most α 4 T , or when the discount factor is at most 1 − 1 α 4 T . See Theorem 3.1 for the formal statement.)
Sentence 2: joint differential privacy [26] is a a relaxation of differential privacy [15,14], it can be applied to many combinatorial problems for which no differentially private algorithm gets non-trivial approximation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The lower level problem in ( 4)-( 5), can be, in principle, addressed by several available solvers.
Sentence 2: finally, we suggest the initialization θ (0) = P Θ (L −1 1 P ×L +n) where n ∼ N (0 P ×L , 0.1L −1 1 P ×L ) in order to be as uninformative as possible regarding the group structure while still breaking the symmetry by adding a small perturbation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This point is crucial for the biological plausibility of this scheme, as it seems unlikely that these minute differences in population response width would be easily measured experimentally.
Sentence 2: we consider a population of N neurons tasked with encoding a probability density over s. One way to do this, known as a kernel density estimate (KDE) code [1,28], is to associate with each neuron a kernel density f n (s) and then approximate the target density with a convex combination of the kernel densities: where x n denotes the firing rate of neuron n and Z = N n=1 e xn .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, if the maximum degree scales as ∆ = O(poly(log p)) and the girth scales as g = O(log log p), then (10) is satisfied.
Sentence 2: (A3) Local-Separation Property: We assume that the ensemble of graphs G(p; η, γ) satisfies the (η, γ)-local separation property with η, γ ∈ N satisfying: where α is given by (7) for Gaussian models and by (8) for Ising models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, ( 6) yields In addition, if ϑ ∈ (0, 1], Lemma 3.2 implies for q := 2 2−ϑ , q := 2 ϑ , a := (n −α c σ 2 −ϑ ϑ ϑ V τ ) 1/2 , and b := (2ϑ −1 E P h f0 ) ϑ/2 , that Since E P h f0 ≥ 0, this inequality also holds for ϑ = 0, and hence (11) shows that we have with probability µ not less than 1 − Ce −τ .
Sentence 2: moreover, several time series models such as ARMA and GARCH, which are often used to describe, e.g.
Relationship: neutral
Domain: NeurIPS
Sentence 1: But following the same approach of rewriting the quantum circuit in the language of Hilbert Space embeddings as in Section 3.2, we get exactly Kernel Bayes Rule [Song et al., 2013]: What we have shown thus far As promised, we see that the two different but valid ways of generalizing Bayes rule for QGMs affects whether we condition according to Kernel Bayes Rule or Nadaraya-Watson kernel regression.
Sentence 2: this is one of the key insights of this paper; showing that Nadaraya-Watson kernel regression is an alternate, valid, but simpler way of generalizing Bayes rule to Hilbert space embeddings.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, since A is not symmetric and positive semi-definite (PSD), A 1 2 does not exist and thus Ax = b cannot be reformulated as Another possible idea is to attempt to find an objective function whose gradient is exactly A t x t − b t and thus the regularized gradient is prox αth(xt) (A t x t − b t ).
Sentence 2: here is a brief roadmap to the rest of the paper.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since U s (t) is varying over time, we can associate each u ∈ U with a |V|-dimensional vector τ u of change points.
Sentence 2: based on the achieved m-by-W jumping-time matrix, we preprocess the feature vectors {g i } m i=1 and k(t ij ), i ∈ {1, . . . , m} , t ij < T , which costs O(mW ) and O(mLW ) where L is the maximum number of events caused by a particular source set before time T . Finally, we apply the projected quasi-newton algorithm [12] to find the weight w that minimizes the negative log-likelihood of observing the given event data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The bounds we provide involve a multiplicative factor that depends on the target rank k. Such a dependence was deemed necessary in non-private settings.
Sentence 2: given a matrix A 2 R n⇥d , output a rank-k orthonormal projection matrix ⇧ such that with probability at least 1 , kA A⇧k p  ↵OPT k (A) + ⌧, where OPT k (A) := min rank(X)k kA Xk p . ( The second main contribution of this paper is an algorithm that returns a differentially private rank-k orthonormal projection matrix with ↵ = O((kd log k) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unfortunately, despite the well-known advantages and recent advancements of multi-way classification techniques [1,19,4] in machine learning, complexity concerns have driven most research on such super large-scale data set back to simple methods such as nearest neighbor search [6], least square regression [16] or learning thousands of binary classifiers [24].
Sentence 2: therefore we argue that the results of our work is not directly comparable with the ILSVRC10 competitions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When the comparator sequence follows the dynamical models closely, P T could be much smaller than P T , and thus the upper bound of Hall and Willett [2013] could be tighter than that of Zinkevich [2003].
Sentence 2: by choosing η = O(1/ √ T ), OGD achieves an O( √ T (1 + P T )) dynamic regret, that is universal.
Relationship: neutral
Domain: NeurIPS
Sentence 1: During training, WNLL activation plays two roles: on one hand, the alternating between linear and WNLL activations benefits each other which enables the neural nets to learn features that is appropriate for both linear classification and WNLL based manifold interpolation.
Sentence 2: moreover, WNLL utilizes both the learned DNNs and the preserved template at test time which seems to be more stable to perturbations on the input data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A grayscale video sequence is a two-dimensional tensor time series because each frame is a two-dimensional array of pixels.
Sentence 2: let p = M m=1 I m and q = M m=1 J m . If A = 0, U 0 = 0, and Q 0 = Q, then the X n of the MLDS become independent and identically distributed draws from the multilinear Gaussian distribution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Input: Initial set of uniformly random samples To preclude such a scenario, we would ideally like to renormalize after each step by doing Ũt ← , where W U DW V is the SVD of matrix U t V t . This algorithm is described in Algorithm 2.
Sentence 2: the following lemma shows the equivalence between Algorithms 2 and 3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given A ∈ R n×d and Q ∈ R m×n with orthonormal columns, Achieving the per vector guarantee of (3) requires a more nuanced understanding of how Simultaneous Iteration and Block Krylov Iteration denoise the spectrum of A.
Sentence 2: frobenius norm error seems an inherent limitation of sketch-and-solve methods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Usually the quality of the predictor ¤ ¦ ¡ ©¨can be measured by a loss function ¦ ¤ §¦ ¡ ¨that is problem dependent.
Sentence 2: assume that ' )( 10 s ut D 75 2 s 2 4 ¨¡ ¤ §¦ ¡ ¨W 8 , then © 8 C W 8 £ G , with probability of at least ¥ $ !
Relationship: neutral
Domain: NeurIPS
Sentence 1: Although the relationship between measured fMRI activity and the spiking activity of neurons is rather complex, as a first-order approximation the fMRI signal can be considered to be monotonically related to the pooled activity of the underlying neural population.
Sentence 2: in our model the complex cell filter bank was implemented by taking the sum of squares of the outputs of four simple cells (corresponding to the wavelet pairs that are identical up to phase), followed by a fixed output nonlinearity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our rejection threshold will be based on a specialization of this estimator, specifically the importance weighted empirical error of a hypothesis h In the notation of Algorithm 1, this is equivalent to where S n ⊆ X × Y × R is the importance weighted sample collected by the algorithm.
Sentence 2: note that both optimizations are over the entire hypothesis class H (with h ′ k only being required to disagree with h k on x k )-this is a key aspect where our algorithm differs from previous approaches.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Comparison of the 2D and 4D results in Table 1 reveals that the relative performance of the heuristics remains unchanged, indicating that the best heuristic for picking experiments is independent of the problem dimension.
Sentence 2: the full GP model can be approximated well by a local GP, where only the k nearest neighbors of the query point are used to compute the prediction value; this reduces the computation time to O(k 3 log(n)) per prediction, since O(log(n)) time is required to find the k-nearest neighbors using spatial indexing structures such as balanced kd-trees.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, to simulate the temporary suppression experiment in [22], we take the original model that had homeostatic regulation applied with all hidden layers intact and developed hallucinations in the process, and clamp the first hidden layer to see whether that would interfere with already established hallucinations.
Sentence 2: we would like to thank Nicolas Heess for helpful comments, Geoff Hinton for input on the mechanism underlying the ACh model (cf.
Relationship: neutral
Domain: NeurIPS
Sentence 1: I-Relief [10,11] is a feature weighting method which cleverly avoids the TN change problem by considering a stochastic variant of NN classifiers (neighborhood component analysis [4] also introduced similar stochastic approximation).
Sentence 2: such TN changes can be easily detected and handled because the TN-weight consistency conditions are represented by a set of linear constraints (see (3c)-(3e)), and we already have explicit rules (Lemmas 5 and 6) for updating the constraints.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the top layer we use Fast Persistent Contrastive Divergence which substantially improved generative performance of GDBNs (see supplementary material for more details).
Sentence 2: generative models have found most success in learning to model small patches of natural images and objects: Zoran and Weiss [4] learned a mixture of Gaussians model over 8×8 image patches; Salakhutdinov and Hinton [2] used 64×64 centered and uncluttered stereo images of toy objects on a clear background; Tang et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The number of Support Vectors (SVs) has a dramatic impact on the efficiency of Support Vector Machines (Vapnik, 1995) during both the learning and prediction stages.
Sentence 2: -Examples such that α * i = C are called bouncing SVs or margin errors and satisfy To illustrate dependence on the Bayes risk, we perform a linear classification task in two dimensions under varying amount of class overlap.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The ability to shift emphasis from one "expert" to another, in response to changes in the observations, is valuable in many applications, including energy management in wireless networks.
Sentence 2: in the general case, the regret bound is: (T − 1) max i D(P (j|i, α * ) P (j|i, α)), where α, α * are now transition matrices, and D(• •) is the relative entropy between discrete distributions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Firstly, tuning a full covariance matrix is time consuming and in our case this adaption process must be carried out simultaneously with searching for an appropriate set of control variables.
Sentence 2: when for the current set of control inputs X c the chain has a low acceptance rate, it means that the variance of p(f |f c ) is still too high and we need to add more control points in order to further reduce G(X c ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Instead of ignoring the dependencies of the activation noise, as in section 3.1, we may retain the dependencies by interpreting dropout (9) as a form of correlated weight noise: where a m is a row of the input matrix and b m a row of the output.
Sentence 2: from this perspective, the marginal distributions (10) then arise through the application of the local reparameterization trick, as introduced in section 2.3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To each function g : X → Y we associate the corresponding loss function f : Z → R defined by f (z) = L[g(x), y] where L is a loss function.
Sentence 2: for a probability distribution ρ on F, define its j-th projection as ρ j = f ∈Sj ρ{f : p j (f ) = f }δ f , where δ f denotes the Dirac measure on f . To shorten notations, we denote the average distance between two successive "projections" by ρd 2 then for any 0 < β < 1/2, with probability at least 1 − β, for any distribution ρ, we have where χ j (x) = 4 x log 4j 2 β −1 log(e 2 /x) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We assume ⇡ 0 (x) = N (0, 2 I) as the initial distribution, and optimize through maximum likelihood.
Sentence 2: in order to achieve high ESS, HMC samplers typically use many leap frog steps and require gradients at every step, which is inefficient when r x U (x) is computationally expensive.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It seems that GNMDS with random input triplets performs best, but for large values of n our kernel function k 1 can compete with it.
Sentence 2: by construction, a single triplet is useless, and what matters is the concurrent presence of two triplets: k 1 (x a , x b ) is only affected by pairs of triplets answering d(x a , x i ) is only affected by pairs of triplets answering (4).
Relationship: neutral
Domain: NeurIPS
Sentence 1: An output unit in the second layer is the maximum of d 2 branch units.
Sentence 2: we denote the first layer input neurons as h ij , with i ∈ {1, 2, . . . , 2m} indexes the branches of second layer neurons, j ∈ {1, 2, . . . , n 0 }.
Relationship: neutral
Domain: NeurIPS
Sentence 1: From a qualitative standpoint, SDA-DP discovers sensible clusters in the data, as demonstrated in Figures 4a-4c.
Sentence 2: the main contributions are a component identification optimization based on a minibatch posterior decomposition, a tractable bound on the objective for the Dirichlet process mixture, and experiments demonstrating the performance of the methodology on large-scale datasets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Though numerous variants of gradient quantization and/or sparsification have been proposed and successfully applied to different deep learning tasks [42,45,37,48,18,7,16], their impact to the convergence rate of distributed SGD (especially for non-convex optimization) is still unclear.
Sentence 2: distributed stochastic gradient descent has been extensively studied in both deep learning and high-performance computing communities, with the goal of accelerating large-scale learning tasks [13,10,9,47,3,14,30,31,6,44,38].
Relationship: neutral
Domain: NeurIPS
Sentence 1: We shall denote by S the K max -selected variables: The computational complexity of the K max -long regularization path of LASSO solutions is Most of the time, we can see that the Lasso effectively catches the true changepoint but also irrelevant change-points at the vicinity of the true ones.
Sentence 2: in this section, we propose to apply our method previously described to real data which have already been analyzed by Bayesian methods: the well-log data which are described in [20] and [6] and displayed in Figure 1.
Relationship: neutral