sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: For example, if the columns of V represent word count vectors for a collection of documents, V f n would be the count of the f th word of the vocabulary in the n th document in the collection.
Sentence 2: it is easy to show (as demonstrated in the supplementary material) that the maximum likelihood estimator for P (f |z) and P n (z) attempts to minimize the Kullback-Leibler (KL) distance between the normalized data distribution V n and P n (f ), weighted by the total count in V n . the model of Equation ( 1) actually represents the decomposition V ≈ WGD = WH (4) where D is an N × N diagonal matrix, whose n th diagonal element is the total number of counts in V n and H = GD.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Finally, just as we have successfully merged HL(λ) with Sarsa(λ) and Watkins' Q(λ), we would also like to see if the same can be done with Peng's Q(λ) [3], and perhaps other reinforcement learning algorithms.
Sentence 2: it would also be good to generalise the result to episodic tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The KECO procedure, described in Algorithm 2 , reduces the computational burden by computing the p-truncated SVD decomposition of the input matrix M via its kernel matrix (lines 3-4) if the number of rows of M is no larger than the number of columns, otherwise the covariance matrix is used (lines 6-8).
Sentence 2: for large data matrices exact SVD decomposition cannot be achieved, so we proposed a computationally efficient procedure to get an approximation that turned to be effective for our goals.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Compared to soft-attention approaches, we loose the ability to naively backprop through read-operations and we have to use approximations like VIMCO.
Sentence 2: we use 2 layered enand decoders with 256 and 128 hidden units with ReLU nonlinearities and a 32 dimensional Gaussian latent variable z.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Continuous Bayes-Adaptive (PO)MDPs have been considered using an online Monte-Carlo algorithm [4]; however this tree-based planning algorithm expands nodes uniformly, and does not admit generalization between beliefs.
Sentence 2: the height map is a draw from a Gaussian process (GP), f ∼ GP (0, K), using a multi-scale squared exponential kernel for the covariance matrix and zero mean.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Building on this observation, a much stronger assertion can be proven for every pair of points in the input space simultaneously: Claim 1 (Uniform convergence of Fourier features).
Sentence 2: if we number the bins of the grid so that a point x falls in bin x = x−u δ and y falls in bin ŷ = y−u δ , then Pr u [x = ŷ|δ] = k hat (x, y; δ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The second ablation experiment tests the necessity of mental updates, without which the model would only attend to the past time steps without passing gradients through them to preceding time steps.
Sentence 2: for the copy task, the network is given a sequence of T + 20 inputs consisting of: a) 10 (randomly generated) digits (digits 1 to 8) followed by; b) T blank inputs followed by; c) a special end-ofsequence character followed by; d) 10 additional blank inputs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the general case, the effectiveness of a particular intervention in a trial participant depends on the inherent effects of the intervention, as well as the participant's expectations (conscious or not).
Sentence 2: put differently, it is always possible that a particular variable which can reveal the nature of the treatment to a trial participant is not identified by the trial designers and thus that no blinding with respect to it is attempted or achieved.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We calculate predictive probability by first setting aside held-out testing documents C (test) from the full corpus and then further setting aside a subset of held-out testing words W d,test in each testing document d. The remaining (training) documents C (train) are used to estimate the global parameter posterior q(β), and the remaining (training) words W d,train within the dth testing document are used to estimate the document-specific parameter posterior q(θ d ).
Sentence 2: indeed, Bayes theorem yields we can calculate the individual minibatch posteriors p(Θ | C b ), perhaps in parallel, and then combine them to find the full posterior p(Θ | C 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: These architectures together with recent large databases (e.g., ImageNet [3]) have obtained astonishing performance on object classification tasks [12,5,20].
Sentence 2: with this database and a standard CNN architecture, we establish new baselines of accuracies on various scene datasets (Scene15 [17,13], MIT Indoor67 [19], SUN database [24], and SUN Attribute Database [18]), significantly outperforming the results obtained by the deep features from the same network architecture trained with ImageNet 1 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our experiments were conducted on heads-up no-limit Texas hold'em, as well as two smaller-scale poker games we call No-Limit Flop Hold'em (NLFH) and No-Limit Turn Hold'em (NLTH).
Sentence 2: if P 1 instead chooses Play, then P 2 may guess how the coin landed.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When the spike input is on (0 < t < t pw ), the dynamics of the circuit for a step input is governed by Equation ( 7) can be changed into a linear ordinary differential equation for i syn (t): In terms of the general solution expressed in (3), we have When the spike input is off (t > t pw ) and we neglect the leakage current from M 2 , then i syn (t) will exponentially decay with the same time constant defined by (11).
Sentence 2: in the following sections, we describe the kinetic model of synaptic conductance, describe the circuit implementation and function, provide a theoretical analysis and finally compare our theory against testing results.
Relationship: neutral
Domain: NeurIPS
Sentence 1: An important open question is to understand the effect of having additional budget to choose multiple coordinates at each time t. The challenge lies in designing appropriate algorithms to invest this budget to update the coordinate selection strategy such that B_max_r performance becomes even closer to max_r.
Sentence 2: [6], and p t i = G i (x t )/G(x t ) [15,14], have also been considered.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Though it is difficult to bound p aprirori, we can check after the solution that our chosen value was sufficient for the global solution, and we have found that very low values (p = 1 or p = 2) were sufficient in our experiments.
Sentence 2: there has been a great deal of work on developing O(k) algorithms that are guaranteed to converge to the LSTD fixed point even in the case of off-policy sampling [16,15].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Several lines of work have focused on consistent estimators for such structurally constrained high-dimensional GLMs.
Sentence 2: sampled from a zero-mean distribution with covariance matrix ⌃ such that for any v 2 R p , the variable hv, X i i is sub-Gaussian with parameter at most  u kvk 2 for every row of X, X i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the next section, we formalize this notion by defining the manifold description of data as a doublet (the shape of the manifold and the projection map).
Sentence 2: presumably, the manifold M has a well defined intrinsic dimensionality d. If we imagine a little ball of radius r centered at some point on the manifold of intrinsic dimensionality d, and then we begin to grow the ball, the number of points on the manifold that fall inside will scale as r d . this will not be necessarily true for the original data set, since it is more spread out and resembles locally the whole embedding space R D . The Grassberger-Procaccia algorithm [12] captures this intuition by calculating the correlation dimension.
Relationship: neutral
Domain: NeurIPS
Sentence 1: By substituting this equality into the equation for computing η k in Algorithm 2, we have Without taking the absolute value, the denominator of ( 12) is ĝ k ĝk−1 / ĝk 2 2 − 1, which is usually negative in stochastic settings.
Sentence 2: we apply SVRG-BB and SGD-BB to solve two standard testing problems in machine learning: logistic regression with 2 -norm regularization (LR), and the squared hinge loss SVM with 2 -norm regularization (SVM): (SVM ) min x where a i ∈ R d and b i ∈ {±1} are the feature vector and class label of the i-th sample, respectively, and λ > 0 is a weighting parameter.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This generalization improvement seems not to depend much on how much of the first network we keep to initialize the second network: keeping anywhere from one to seven layers produces improved performance, with slightly better performance as we keep more layers.
Sentence 2: we also document that the transferability of features decreases as the distance between the base task and target task increases, but that transferring features even from distant tasks can be better than using random features.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , X n ∈ R p and a column y ∈ R n . We will assume that each X i 1 ≤ 1 and |y i | ≤ 1.
Sentence 2: before we formally introduce the covariance perturbation algorithm due to [19], observe that the optimal solution θ * can be computed as θ * only depends on the private data through X y and X X.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The histograms clearly show that the model on the left failed to generate all classes (loss in recall), while the model on the right is producing a more balanced distribution over all classes (high recall).
Sentence 2: fID has been shown to be robust to image corruption, it correlates well with the visual fidelity of the samples, and it can be computed on unlabeled data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We use Σ CL = CL( Σ) and E CL = CL E ( Σ) to denote respectively the covariance matrix and the set of edges learned using the Chow-Liu algorithm where the samples have empirical covariance matrix Σ.
Sentence 2: using Algorithm 3, the objective function of (3) decreases with the number of iterations, i.e., D KL (N (0, ΣT )||N (0, Σ )) ≤ N (0, ΣT )||N (0, Σ T )).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the subsequent sections, we present a model of the ventral stream that is consistent with a large body of experimental results 1 and additionally predicts the existence of discrete face-selective patches organized in this manner.
Sentence 2: within the class of faces, knowledge of the image transformation evoked by 3D rotation can be reliably transferred from previously viewed faces to help identify a novel face at a new viewpoint.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We solve this problem using MAP inference via EM with a mean-field variational approximation q(x) to the posterior p(x|y, B) [13], where q(x) The E-step, after observing that for binary x, /q 0 ), q 0 = k/M , the vector c = diag(B T B), and C = B T B − diag(c), i.e.
Sentence 2: we first propose its computational function as recovery of high-dimensional sparse olfactory signals from a small number of measurements.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Random search is a natural baseline to compare optimisation methods.
Sentence 2: x i ∈ X , y i = f (x i ) + i ∈ R, and i ∼ N (0, η 2 ), the posterior process f |D n is also a GP with mean µ n and covariance and K ∈ R n×n with K i,j = κ(x i , x j ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: All models share a common w. We make a few additional assumptions.
Sentence 2: firstly, initialize w with a wide Gaussian profile, then estimate e KA e K H from element-wise division of C mele by f W . Secondly, use SVD to decompose e KA e K H into an orthogonal base set e K and a positive diagonal matrix A, where e K and A contain information about k i 's and ↵'s respectively, hypothesizing that k's are orthogonal to each other and ↵'s are all positive (Assumptions 3 and 5).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We should stress in particular that whenever we say that the set of OGDA-stable fixed points is a super-set of the GDA-stable fixed points, we will be somewhat abusing notation, since the fixed points of OGDA lie in R 2n+2m while the fixed points of GDA lie in R n+m .
Sentence 2: let (x * , y * ) be a local min-max critical point of f and matrix H (see equations ( 5)) computed at (x * , y * ) has all its eigenvalues with real part nonzero (i.e., Assumption 1.8).
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the true label is Y = 0, then the attempted labeling is much more likely to fail, but because of noise, could succeed.
Sentence 2: for a two-component mixture sample, M , and a sample from one of the components, C, it only requires an algorithm to estimate the maximum proportion of C in M . For this purpose, we use the AlphaMax algorithm (Jain et al., 2016), briefly summarized in the Appendix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, this curious property appears anytime the variables take the form Y = BG, for any fixed scalar random variable B and Gaussian vector G. It follows that the predictive mean estimates for (10) employing sub-Gaussian priors are identical to the estimates under a Gaussian hypothesis.
Sentence 2: our discussion of the stable process regression problem has principally been confined to an exposition of the basic theoretical issues and principles involved, rather than to algorithmic procedures.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The idea is simple: instead of choosing a (potentially different) expert at each stage of the game, the number of stages an expert is followed, each time it is selected, increases gradually.
Sentence 2: (b) When lim sup i→∞ M e (i) < V , there is a phase I such that for all i ≥ I, M e (i) < M Ē (i), so that expert e is played only on exploration phases, and a large deviations argument establishes that (3) holds.
Relationship: neutral
Domain: NeurIPS
Sentence 1: On the other hand, from the computational point of view, our procedure is quite comparable with the direct stochastic gradient descent.
Sentence 2: at each iteration i, a new data point (X i , Y i ) is observed and there are two updates: one is the value ζ i as the result of the stochastic gradient descent in the dual space, the other is the update of the parameter θ i which is the "mirror image" of ζ i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: It does so by computing messages in a message-passing algorithm using Monte Carlo sampling, freeing us from having to implement hand-crafted message update operators.
Sentence 2: in addition to the difficulty of computing messages for the multidimensional yield factor, inference in the model is challenging as it includes multiple Gaussian processes, separate t opt and y max variables for each location, many copies of the yield factor, and its graph is loopy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To address such a problem, a popular approach is to assume the covariance matrix of the tensor normal distribution is separable in the sense that it is the Kronecker product of small covariance matrices, each of which corresponds to one way of the tensor.
Sentence 2: we define kAk 1,off := P i6 =j |A i,j | as its off-diagonal `1 norm and |||A||| 1 := max i P j |A i,j | as the maximum absolute row sum.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this section, we extend this definition of sleeping regret to sleeping transductive regret, that is the difference between the learner's cumulative expected loss and the cumulative expected loss of any transduction of the learner's actions among a family of finite-state transducers, where the weights of the transductions are normalized over the set of awake experts.
Sentence 2: this is because the true losses assigned to each column of the stochastic matrix are the same, and the rescaling based on the distribution p t is uniform over each row.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It follows from Lemma 3 and Lemma 1 that, if u i = 0, then x * i = 0.
Sentence 2: for example, with the grouping by pathways, FoGLasso is about 25 and 70 times faster than SLasso for 1000 and 2000 genes, respectively; and 3) the efficiency on edges is inferior to that on pathways, due to the larger number of overlapping groups.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Substituting yields Note that 1) ρ is the empirical distribution over the observations, and so converges almost surely (a.s.) to the true generating distribution, and 2) the convergence properties of P n are determined by the quantity between the square brackets in (2).
Sentence 2: the results of a   This paper has introduced the problem of dynamic coherence and analyzed it when the dynamics are induced by Bayes' rule.
Relationship: neutral
Domain: NeurIPS
Sentence 1: where W is the adjacency matrix, finding the minimum bisection of G is equivalent to finding a partition of G that minimizes the SRcut cost function with weights β = e and the regularization parameter α > d * where Proof: Without loss of generality, we assume that N is even (if not, we can always add an isolated vertex).
Sentence 2: the corresponding SRcut value is then computed.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The ith input sample is given as x i = (s i , t i , w i ), which is a combination of task index (s i , t i ) and input feature w i .
Sentence 2: first, we assume that the distribution P (X) of the input feature x ∈ X is a product measure of P k (X) on each X k . P X (dX This is typically assumed in the analysis of linear tensor estimation methods [13,6,3,21,1,36,27,37].
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the era of big data, searching for the desired information has become an important topic in such a vast ocean of data.
Sentence 2: dCC which is used to solve the discrete optimization by DSDH, can only be applied to the standard binary quadratic program (BQP) problem with limited applications, while HashNet is still distracted by quantization error as β cannot increase infinitely.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When all blocks have size one, or equivalently when all kernel matrices have rank one, then the path is provably linear in 1/λ between each kink [4] and is thus easy to follow.
Sentence 2: the path is obtained by using numerical continuation techniques, and involves a running time complexity that is a constant times the complexity of solving the problem for one value of the regularization parameter.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We labelled a subset of 100 out of the total of 698 data-points with the three mentioned degrees of freedom in the following way: After standardizing the pose and lighting parameters so that they were centered and had unit variance, we constructed three corresponding similarity matrices (P Pose1 , P Pose2 , P Lighting ) for a randomly chosen subset of 100 points using Eq.
Sentence 2: both these difficulties can be alleviated by allowing the user to provide more information than just the raw data points or a single set of pairwise similarities between data points.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We also obtain a valid approximation, of course, without selection (I = {1,. . . ,H}) but MCMC samplers in very high dimensional spaces  ); compute M-step with arguments f (� s) as in ( 3) and (4); until (until Θ have converged); Illustration of general application.
Sentence 2: 2) and they show that spike-and-slab models may be very suitable generalized V1 models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure 1 (d) and (h) show that both models achieve the desired mean population sparsity.
Sentence 2: the benefit of using RBMs as building blocks for a DBN is that they often provide a good initialization for feed-forward neural networks, and they can effectively utilize large amounts of unlabeled data, which has led to success in a variety of application domains [3].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Consequently, we evaluate the performance of an estimate θ using log-loss on a held-out dataset.
Sentence 2: let θ denote the vector output by any of our procedures after inference (so in the BAVGM case, for example, this is the vector θ = θ BAVGM = (θ 1 − rθ 2 )/(1 − r)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our results indicate that by leveraging the network interaction structure, it is possible to tolerate noise with variance that increases with the size of the network whereas without exploiting dependencies in the node measurements, the noise variance needs to decrease as the network size grows to accommodate for multiple hypothesis testing effects.
Sentence 2: by Markov's inequality, for t > 0,  Note that x contained within the ellipsoid x T Lx ≤ δp, x ∈ {0, 1} p implies that x is feasible, so a solution to the optimization upper bounds sup x:x T Lx≤δp p i=k+1 (u T i x) 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For rotation matrices it is computed as the Frobenius norm of the difference between ZT Z and Gaussian noise variance Mean 3D error [mm] GP GP + trsf Cstr GP [12] Cstr GP [12]    Gaussian noise variance Mean 3D error [mm] GP GP + trsf Cstr GP [12] Cstr GP [12]   Note that the global transformations estimated with the PnP method yield poor reconstructions.
Sentence 2: note, however, that other types of image information, such as silhouettes or texture, could also be employed.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The online classification algorithms discussed above keep enlarging C t -once an example is added to C t it will never be deleted.
Sentence 2: examples of such algorithms include the Relaxed Online Maximum Margin Algorithm (ROMMA) [4], the Approximate Maximal Margin Classification Algorithm (ALMA) [2], and the Margin Infused Relaxed Algorithm (MIRA) [1] which can be used in conjunction with kernel functions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is known that these two coincide up to a change of the regularization coefficient.
Sentence 2: we show that (i) as a direct result of feature-wise independence of the uncertainty set, a slight change of a feature that was originally assigned zero weight still gets zero weight (Theorem 4); (ii) using Theorem 4, we show that "nearly" orthogonal features get zero weight (Corollary 1); and (iii) "nearly" linearly dependent features get zero weight (Theorem 5).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We use a subset that consists of 22,395 records of patients over age 15 and stayed in ICUs between 2001 and 2012, among which 2,624 patients are diagnosed of sepsis.
Sentence 2: we utilize variational inference, which is an approximation method that has been shown to be successful in many applications of neural networks [16,23], along with reprameterization tricks for pathwise backpropagation [15,8].
Relationship: neutral
Domain: NeurIPS
Sentence 1: The internal reward features are capable of representing arbitrary policies (and thus we also implemented classical policy gradient with these features using OLPOMDP [2] but found it to be far slower than the use of PGRD with UCT and hence don't present those results here).
Sentence 2: in a departure from the original definition of the routing domain, we parameterize the transition function to allow a comparison of agents' performance when transition functions change.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We focus on a graphical variant defined as follows: There exist some graph G whose vertex set is the set of arm K and an arbitrary edge set E. For every sub-optimal arm x there exist some neighbor y in the graph such that µ(x) < µ(y).
Sentence 2: indeed, one cannot discover the best arm without verifying that it is superior to the others, and the set Y provides the best strategy to do so.
Relationship: neutral