sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Uniformly randomly pick a set I t from {1, . . . , N} (with replacement) such that |I t | = b 5: Randomly draw η t ∼ N (0, h t ) 6: α i t+1 = θ t for i ∈ I t and α i t+1 = α i t for i / ∈ I t 8: The increased variance in SGLD is due to the fact that we only have information from n N data points at each iteration.
Sentence 2: inspired by a minibatch version of the SAGA algorithm [5], we can include information from the remaining data points via an approximate gradient, and partially update the average gradient in each operation.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: With the proposed lattice models, one can constrain f (x) to have a ceterus paribus diminishing returns response in the number of guests (for any fixed number of bottles) or in the number of bottles of wine (for any fixed number of guests), but without forcing f (x) to have a diminishing returns response along the diagonal direction defined as one bottle of wine per guest.
Sentence 2: with the proposed SCNN, imposing diminishing returns on both wine and guests produces joint concavity, such that f (x) will be concave and decreasing over any line in the two-dimensional feature space.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: While the algorithm is efficient, it cannot be immediately formalized as a cost function with global solution, it relies solely on 2d information, and the affinity functions are handcrafted.
Sentence 2: we provide a method that leverages a volumetric 3d scene representation with learned scoring functions for the component parts, and an efficient global linear integer programming solution for person grouping with kinematic constraint generation, and amenable to efficient solvers (e.g.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: At each time step, SQL uses two successive estimates of the action-value function that makes its space complexity twice as the standard Q-learning.
Sentence 2: this allows SQL to use a more aggressive learning rate for one of the terms in its update rule and eventually achieves a faster convergence rate than the standard Qlearning (see Section 3.1 for a more detailed discussion).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the applied psychology literature, awareness of sequential dependencies has led some researchers to explore strategies that mitigate relativity of judgment, such as increasing the number of response categories and varying the type and frequency of anchors (Mumma & Wilson, 2006;Wedell, Parducci, & Lane, 1990).
Sentence 2: our approach to extracting more information from human judgments is to develop automatic techniques that recover the underlying sensation from a response that has been contaminated by cognitive processes producing the response.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The algorithms presented in [2] determine this point, which is the exponential loss solution x boost £ Xy 3¥ a cb `d ) 4 9 Bv w C i zG (see Figure 1, left).
Sentence 2: maximum conditional likelihood estimation for an exponential model with the same features is equivalent to the problem x ml £ y ¦ ¥ a cb ¤d ) 4 #" 9 v w C zG where £¢ u is the exponential family with additional Lagrange multipliers, one for each normalization constraint.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If we do not consider running time, we could construct a low-rank approximation to A as follows: since projecting TAS onto W T is approximately optimal, it follows from Lemma A.1 that with probability 98/100, Let (AS) k = PN T be such that P has orthonormal columns.
Sentence 2: then, AS − PP T AS 2 F = AS − (AS) k 2 F and by Lemma A.1 it follows that with probability 98/100, A − PP T A 2 F ≤ A − A k 2 F + A F . even approximately computing a column space P for (AS) k using an input-sparsity time algorithm is no longer sublinear.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In other words, measuring the effect of ⇣ m,j on @L SGVB D /@b m,j is easy as ⇣ m,j is the only random variable directly influencing this gradient via b m,j .
Sentence 2: when sampling random weights, there are a thousand ✏ i,j influencing each gradient term, so their individual effects get lost in the noise.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: we introduce a dummy variable gj such that if Y = j, then gj Ix = 1, otherwise gj Ix = 0, where j = 1,•••, J.
Sentence 2: we since there may not be any data at Xi = z, the data from the neighborhood of x along dimension i are used to estimate E[gj IXi = z], a strategy suggested in [7].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The resulting high-order terms inside the expansion step also take the form (1) (in fact, Corollary 1 applies here); with no need to build the 'full' high-order graph, this would allow α-expansion to work as a fast alternative to the classic greedy algorithm for facility location, very similar to the fusion-based algorithm in [4].
Sentence 2: in Section 3.2 we show that our generalized transformation allows for a novel way to optimize a hierarchical facility location objective.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, if P is B(2/3) over h and t, then for n = 3, P ({3}) = P (hhh) + P (ttt) = 1/3, P ({2, 1}) = P (hht) + P (hth) + P (thh) + P (tth) + P (tht) + P (htt) = 2/3, and P ({1, 1, 1} = 0 as this P is binary hence at most two symbols can appear.
Sentence 2: if P is a roll of a fair die, then P ({3}) = 1/36, P ({2, 1}) = 5/12, and P ({1, 1, 1} = 5/9.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In other words, if H contains a very good policy that has little support under π, we will not be able to detect that by our estimator.
Sentence 2: our estimation is safe in the sense that we will never drastically overestimate the value of any policy in H. This "underestimate, but don't overestimate" property is critical to the application of optimization techniques, as it implies we can use an unrestrained learning algorithm to derive a warm start policy.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Similarly, as an inductive component of Low Density Separation (LDS) [11], ∆ TSVMs learns the SVM classification model in the primal, which can be used for predicting new data.
Sentence 2: the graph part of LDS is transductive, because the kernel and the graph distances are addressed by a prior eigen-decompostion and re-representation (MDS); thus, it is unclear how to make a prediction of a new test point other than by rebuilding the graph with the new test point.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: It was pointed out in [5] that if supp 0 ( ŵ) can exactly identify all non-zero components of the target vector, then in the second stage, the relaxed Lasso can asymptotically remove the bias in the first stage Lasso.
Sentence 2: it is not clear what theoretical result can be stated when Lasso cannot exactly identify all relevant features.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Conversely, for the Cambermet, Chimet and Bramblemet sensors, MOSM and CSM provided similar results, though we cannot confirm their difference is statistically significant.
Sentence 2: given the high correlation of these signals and the similarity between the MOSM model and the CSM model, the close performance of these two models on this dataset is to be expected.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: samples from an unknown distribution (6) with parameter ✓ ⇤ , one could consider estimating the graphical model structure with an `1-regularized , and where we have collated the edgewise parameters {✓ st;jk } m j,k=1 for an edge (s, t) 2 E into the vector ✓ st .
Sentence 2: there is an critical caveat to actually computing this regularized MLE: the computation of the log-partition function A(✓) is intractable (see [18] for details).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: (2) The distribution of s is aN-dimensional manifold embedded in aM-dimensional vector space and nominally has a negatively divergent entropy.
Sentence 2: as shown in Appendix 1, the probability density of s can be related to the input distribution via the relation: where the susceptibility (or Jacobian) matrix X is defined as: This result can be understood in terms of the singular value decomposition (SVD) of the matrix x.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We improved this result by providing a finite-sample bound with optimal rate of convergence and also analyzed the quality of approximation in L r -norm (1 ≤ r < ∞).
Sentence 2: we also proposed an RFF approximation for derivatives of a kernel and provided theoretical guarantees on the quality of approximation in uniform and L r -norms over compact subsets of R d . While all the results in this paper (and also in the literature) dealt with the approximation quality of RFF over only compact subsets of R d , it is of interest to understand its behavior over entire R d . as discussed in Remark 1(ii) and in the paragraph following Theorem 3, RFF cannot approximate the kernel uniformly or in L r -norm over R d . By truncating the Taylor series expansion of the exponential function, [3] proposed a non-random finite dimensional representation to approximate the Gaussian kernel which also enjoys the computational advantages of RFF.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: An example of a divergence which satisfies the assumption of strong convexity and smoothness of over R d is the Mahalanobis distance which is a divergence induced by the function (x) = x T Ax, for some positive definite matrix A.
Sentence 2: we note that many popular divergences such as KL-divergence do not satisfy the smoothness condition over the entire space R d . For such divergences, depends on the distance between the starting point ✓ 0 and the minimizer ✓ and their location in the space.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ROVER calculates the optical flow of consecutive radar maps using the algorithm in [5] and performs semi-Lagrangian advection [4] on the flow field, which is assumed to be still, to accomplish the prediction.
Sentence 2: the success of these optical flow based methods is limited because the flow estimation step and the radar echo extrapolation step are separated and it is challenging to determine the model parameters to give good prediction performance.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: . . , T T , such that depth(T t ) may equal t. Furthermore, the number of new nodes added to the tree on round t is on the order of t, resulting in T t having O(t 2 ) nodes.
Sentence 2: pST implementation tricks in [1] can be used to reduce the space complexity of the algorithm from quadratic to linear in t. The online learning algorithm presented in the previous section has one major drawback, the PSTs it generates can keep growing with each online round.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: gap_per_epoch performs poorly because it is unable to adapt to the variability of the coordinate-wise duality gaps G i that vary a lot from one iteration to the next.
Sentence 2: this variation slows down the convergence of B_max_r compared to max_r, but B_max_r is still able to cope with this change by exploring and updating the estimations of the marginal decreases.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The resulting algorithm is passive whenever the loss is zero, that is, w t+1 = w t whenever (w t ; z t ) = 0.
Sentence 2: on rounds for which (w t ; z t ) > 0 we aggressively force w t+1 to satisfy the constraint (w t+1 ; z t ) = 0.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given a prior, the Bayes optimal estimators are known to be the posterior mean under MSE, the Maximum A Posterior (MAP) rule under 0/1 loss, and the posterior centroid under Hamming loss [8].
Sentence 2: these estimators and their corresponding risks (expected loss) have no closed form for the Ising graphical model and are intractable to analyze.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Of course, this cannot exactly accomplish optimal resampling, both because the chance that a particle survives should be normalized with respect to the population, and because the distribution from which a non-surviving particle resamples should also depend on the ensemble distribution.
Sentence 2: it has a similar qualitative effect of suppressing conditionally unlikely samples and replacing them ultimately with conditionally more likely ones.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Since for α small enough d M,α (r, r) > 0 for any r such that h(r) > 0, Sinkhorn distances cannot satisfy the coincidence axiom (d(x, y) = 0 ⇔ x = y holds for all x, y).
Sentence 2: multiplying d M,α by 1 r =c suffices to recover the coincidence property if needed.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As shown in (3), this allows for a modular representation of Q π in which the MDP's dynamics are decoupled from its rewards, which are captured by the weights w. One potential benefit of having such a decoupled representation is that only the relevant module must be relearned when either the dynamics or the reward changes, which may serve as an argument in favor of adopting SFs as a general approximation scheme for RL.
Sentence 2: in this paper we focus on a scenario where the decoupled value-function approximation provided by SFs is exploited to its full extent, as we discuss next.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Similarly, under the setting of domain adaptation, standard binary adversarial cost Lempitsky, 2015, Ganin et al., 2016] and central moment discrepancy (CMD) [Zellinger et al., 2017] have been utilized to learn features that are domain invariant.
Sentence 2: all these invariance inducing criteria suffer from a similar drawback, which is they are defined to measure the divergence between a pair of distributions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In order to utilize the auxiliary function of the estimating function for the gNG, we defined an auxiliary function on the criterion of the near optimality of the estimating function, by minimizing the distance between the immediate reward as the regressand and the subspace of the regressors of the gNG at the solution of the gNG.
Sentence 2: it may be possible to use different criterion, such as the optimality on the Fisher information matrix metric instead of the Euclidean metric.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: More importantly, [11] proposes a specific initialization using which the alternating minimization method is shown to converge linearly in noise-free PR and CPR.
Sentence 2: the number of measurements required to establish this convergence is effectively quadratic in k. In [12] and [13] the 1 -regularized form of the trace minimization is proposed for the CPR problem.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Prior to this work, Lipschitzian error bounds for composite function minimization are available for cases where the non-smooth part either has a polyhedral epigraph (such as the ℓ 1 -norm) [23] or is the (sparse) group LASSO regularization [22,25].
Sentence 2: the question of whether a similar bound holds for trace norm regularization has remained open, despite its apparent similarity to ℓ 1 -norm regularization.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Racing algorithms (e.g., [10,12]) and action-elimination algorithms [7] address this problem under a constraint on the accuracy in identifying the best arm and they minimize the budget needed to achieve that accuracy.
Sentence 2: uCB-E and Successive Rejects are designed for a single bandit problem, and as we will discuss later, cannot be easily extended to the multi-bandit case studied in this paper.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The reason is because the objective function in ( 6) is a linear function in p. Hence, we can simply obtain s k,DUDE (c, •) = arg max s p(c) s , where p(c) s stands for the s-th coordinate of p(c).
Sentence 2: as seen in the previous section, DUDE utilizes the estimated loss matrix L, which does not depend on the clean sequence x n . the main drawback of DUDE is that, as can be seen in ( 5), it treats each context c independently from others.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For example, the method in Fearnhead and Rigaill [12] only produces point estimates and is limited to fitting a piecewise constant function to univariate data.
Sentence 2: bOCPD can be applied to multivariate data and a set of models M while quantifying uncertainty about these models, their parameters and potential CPS, but is not robust.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: So we have: £ 1 a mx@t £ 1 x; 0A; £ 2 a mx@x t £ 1 w; 0A A v £ a min @mx@@x t £ 1A=; 0A ; wA : This expresses v £ as a function of the unknown optimal dual variable t £ .
Sentence 2: for the simple case of 2-potentials, we can solve for t £ explicitly and get a closed form expression: 2 @e kl C 1 @xk xlA@e k e l AA if jxk xlj < in general to find t £ we note that v £ must satisfy v £ ¡ 1 a y.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In recent work, Chan et al [CDSS14] presented an approach employing an intricate combination of dynamic programming and linear programming which yields a poly(k/") time algorithm for the above problem.
Sentence 2: the running time of the [CDSS14] algorithm is ⌦(k 3 ) even for constant values of ", making it impractical for applications.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Moreover it has to be remarked that this tightening of the bound does not appear to deliver any reduction in the capabilities to select a good model (such a case would imply that we can predict more accurately a bigger error rate, but our bound is able to predict accurately the same error rate as the PAC-Bayes Bound).
Sentence 2: 0.025 ± 0.004 0.030 ± 0.007 0.038 ± 0.005 0.036 ± 0.007 0.038 ± 0.005 10 0.020 ± 0.007 0.021 ± 0.007 0.021 ± 0.007 0.025 ± 0.008 0.026 ± 0.008 100 0.020 ± 0.007 0.021 ± 0.007 0.021 ± 0.007 0.025 ± 0.008 0.026 ± 0.008 500 0.020 ± 0.007 0.021 ± 0.007 0.021 ± 0.007 0.025 ± 0.008 0.025 ± 0.005 the comparison with Table 5 points out that the PAC-Bayes bound is not as accurate as Ten Fold cross-validation when it comes to selecting a model that yields a low test error rate.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Previously this game has been solved asymptotically as both T and K tend to ∞: asymptotically the upper bound on the performance of the state-of-theart Multiplicative Weights Algorithm (MWA) for the learner matches the optimal multiplicative constant of the asymptotic minimax optimal regret rate � (T /2) log K [3].
Sentence 2: for finite K, this asymptotic quantity actually overestimates the finite-time value of the game.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The distinguishing feature of judgments relative to other kinds of decision problems is that they are asymmetric; if I apply for a loan and I get the loan, I am satisfied, and do not particularly care for an explanation; even the bank may not care as long as on aggregate the algorithm makes the bank money.
Sentence 2: i very much care if the algorithm denies my mortgage application.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Similar to the blind source separation case, our metric clearly does not necessarily converge to the Hessian and so it is not necessarily asymptotically efficient (ie does not attain a second order convergence rate).
Sentence 2: in general, the Hessian will not be positive definite and so the curvature it provides could be of little use until B is close to a local maxima.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We also considered a control model ("Time Decay"), described in Section 2, that produces temporal dynamics by learning time constants on the activations at each layer, rather than by learning connectivity between units.
Sentence 2: this model did not perform any better than the basenet, implying that ConvRNN performance is not a trivial result of outputting a dynamic time course of responses.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For instance, exemplars 0111 and 0001 were given lower ratings in the common-cause and common-effect conditions , respectively (39.4 and 26.3) than in the control condition (67.6 and 67.0) presumably because in these exemplars correlations are broken (effect features are present even though their causes are absent).
Sentence 2: exemplar 1111 received a significantly higher rating in the common-cause and common-effect conditions than in the control condition (90.8 and 9l.0 vs. 75.6) , presumably because in both conditions all correlations are preserved.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In the case of GRAVITAR, even though both A3C and A2C, which are policy gradient methods, have a lower score than valuebased DQN, G2AC achieves a higher score with less frames of training.
Sentence 2: for SEAQUEST, it seems that G2AC is not able to deviate from the local minima, scoring a similar rewards as A2C.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: On the one hand, they need to train a lot of iterations since DSDH updates the hash code bit-by-bit, while HashNet requires to increase β iteratively.
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: contrasting
Domain: NeurIPS
Sentence 1: However, in certain subclasses of MRF, an optimal or close-to-optimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods.
Sentence 2: these solutions do not apply to the many MRFs that contain such tractable components as sub-networks, but also other non-complying potentials.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Both of the reformulated problems do not require backpropagation algorithm at all and are easy to be parallelized.
Sentence 2: neither of  Figure 1: Illustrations of the backward pass of the backpropagation algorithm (BP) [30], decoupled neural interface (DNI) [13] and decoupled parallel backpropagation (DDG) [11].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Robust algorithms have been exhibited for mean and covariance estimation and clustering (Diakonikolas et al., 2016;Lai et al., 2016;Charikar et al., 2017), classification (Klivans et al., 2009;Awasthi et al., 2014), regression (Nasrabadi et al., 2011;Nguyen and Tran, 2013;Chen et al., 2013;Bhatia et al., 2015) and crowdsourced data aggregation (Steinhardt et al., 2016).
Sentence 2: these bounds only hold for specific (sometimes quite sophisticated) algorithms and are focused on good asymptotic performance, rather than on giving good numerical error guarantees for concrete datasets/defenses.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In a sense, the argument above demonstrates the fact that in most "interesting" IDS games (those in which each player is a true participant, and can have their behavior swayed by that of the overall population), there are two trivial pure NE (all invest and none invest).
Sentence 2: we are also interested in finding NE in which some players are choosing to invest and others not to (even though no player has a dominant strategy).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: When the time required to lock memory for writing is dwarfed by the gradient computation time, this method results in a linear speedup, as the errors induced by the lag in the gradients are not too severe.
Sentence 2: we note that in many applications of interest in machine learning, gradient computation time is incredibly fast, and we now demonstrate that in a variety of applications, HOGWILD!
Relationship: contrasting