sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: The learning algorithm learns the parameters of the individual labelers, and uses them to decide which labeler to query for each example.
Sentence 2: algorithm 5 generates a Ŝk such that the set V k defined as: has the property that: This is achieved by labeling, through inference or query, a large enough sample of unlabeled data drawn from U. Labels are obtained from three sources -direct inference (if x lies outside the disagreement region as identified by Algorithm 4), querying O (if the difference classifier predicts a difference), and querying W . How large should the sample be to reach the target excess error?
Relationship: neutral
Domain: NeurIPS
Sentence 1: We conduct experiments on a large-scale dataset [17] for conversation question answering, which consists of 200K dialogs with 1.6M turns over 12.8M entities from Wikidata.
Sentence 2: since previous questions and answers/responses in conversation are useful contexts, we concatenate them with the current question as an input x = (x 1 , ..., x T ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each particle in our SMC algorithm is a sequence of states and waiting times for the current sequence k. By using a Particle MCMC (PMCMC) method [1], we then compute an acceptance ratio that makes this proposal a valid MCMC move.
Sentence 2: the application of non-parametric Bayesian techniques to time series has been an active field in the recent years, and has led to many successful continuous time models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Similarly to Theorem 2 in (Abbasi-Yadkori, Pal, and Szepesvari, 2011) 2 , for any state history and with probability of at least 1 − δ, it holds for all t > 0 that θT t,a x(s t ) − θ * a T x(s t ) ≤ we define δ = δ/k and bound this probability for all the actions, i.e., ∀a, t > 0 Recall that any valid action a at state s satisfies E[e t (s, a)] = θ * a T x(s t ) ≤ .
Sentence 2: a practical challenge here is that the features must be fixed over time when used by the contextual bandit, while the activations change during optimization.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The second component is the addressing variable a 2 {1, ..., |M|} which selects a memory entry m a from the memory buffer M. The varitional posterior distribution q(a|x) is parameterized as a softmax over a similarity measure between x and each of the memory entries m a : where S q (x, y) is a learned similarity function described in more detail below.
Sentence 2: since we have a discrete latent variable a in the model we can not simply backpropagate gradients through it.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show that (i) the problem (4) can be solved within O( P 0 (k + log( P 0 )) + (n + m)k 2 ) time, where k is the rank of X, and (ii) the algorithm converges to the critical points of f (X, d).
Sentence 2: we also vary r in the range {10, 20,  Accuracy Figure 1(a) and 1(b) clearly show that the proposed algorithm can perfectly recover the underlying inter-purchase durations with varied numbers of users, items, and categories.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In a detailed study on AMS-based broad-band SNR estimation [11) it was shown that harmonicity which is well represented in AMS patterns is the most important cue for the neural network to distinguish between speech and noise.
Sentence 2: the input matrix consists of 5 times the auditory model feature vector with 30 elements, glued together in order to allow the network to memorize a time sequence of input matrices.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Using straightforward algebra and the Sherman-Morrison inverse formula, we can show that the resulting solution to the minimization of (2.1) is: where The detailed derivation will appear in a longer version.
Sentence 2: the results show that the accuracy achieved by our LEGO+LSH algorithm is comparable to the LEGO+linear scan (and similarly, L 2 +LSH is comparable to L 2 +linear scan), thus validating the effectiveness of our online hashing scheme.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We formalize this problem as that of decomposing X into two constituent graphs E 1 and E 2 , the true and the noise graphs respectively, such that e We use a training set to fit our model parameters and then measure task performance on a test set.
Sentence 2: we test our model on the task of discerning which of the edges in X are also in Y gold .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this case, the Kullback-Leibler divergence of projection (1) of P on (T, C) from P is bounded [13]: This bound means that if we have an ε-junction tree for P (V ), then instead of P we can use its tractable principled approximation P (T,C) for inference.
Sentence 2: we can get a probabilistic estimate of I (A, B | C), that has accuracy ±∆ with probability 1 − γ, using number of samples and computation time polynomial in 1 ∆ and log 1 γ : Theorem 11.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hence a natural question to ask is: given a point cloud in N -dimensional Euclidean space, what is the dimension of the manifold that best captures the structure of this data set?
Sentence 2: if we choose a sufficiently small value for δ and ρ, we are guaranteed estimation accuracy levels as close as desired to those obtained with ID estimation in the original signal space.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To match the fact that our image contrast distribution is zero mean Gaussian, and therefore symmetric about the origin, we pair the types into two pairs of equal-size populations and keep the number of cells the same across each pair during this optimization, expecting that ON and OFF homologous types will emerge.
Sentence 2: the total density of cells varies across eccentricity by 3 orders of magnitude in the primate retina.
Relationship: neutral
Domain: NeurIPS
Sentence 1: First we bound the difference between the target risk ǫ T (h) and weighted risk ǫ α (h).
Sentence 2: the proofs of these lemmas, as well as the proof of Theorem 2, are in Appendix B. Lemma 1 Let h be a hypothesis in class H. Then The lemma shows that as α approaches 1, we rely increasingly on the target data, and the distance between domains matters less and less.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As a common means to encouraging sparsity in machine learning, the 1 norm has been incorporated into the NMF objective function [6] as a sparsity regularizer.
Sentence 2: in this work, we focus on the generalized Kulback-Leibler divergence (a special case of the Bregmann divergence), and use its decomposing property to simplify the mfNMF objective and remove the undesirable multitude of equivalent solutions in the general formulation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our contribution is based on a generalized view of state estimation that subsumes the naïve, piecewisetrained models discussed in the previous section and allows them to be trained end-to-end using simple and scalable stochastic gradient descent methods.
Sentence 2: because the dynamics model is non-linear, we equipped our model-based state estimators with extended Kalman filters, which is a straightforward addition to the BKF framework.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Surprisingly, for approximate representation, the conditional gradient algorithm can approximate any homogeneous mixture within accuracy by combining O(1/ 2 ) shallow models, where the hidden constant may decrease exponentially wrt the depth.
Sentence 2: the nonnegative rank characterizes the smallest size of shallow SPNs (LCMs) that represent the density mixture W. Similarly, we can prove the following result when the leaf nodes are from F instead of the convex hull G. Theorem 4.2.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The idea is to attach numerical quantities to persistence barcodes, which can then be used as input to any machine learning algorithm in the form of feature vectors.
Sentence 2: [13] restrict F to functions on a unit ball in H , i.e., F = { f ∈ H : f ∞ ≤ 1}, and show that Eq.
Relationship: neutral
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: as such, it provides stronger guarantees: instead of comparing the performance of π with that of the previously-computed policies π j , Theorem 2 quantifies the loss incurred by following π as opposed to one of M i 's optimal policies.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, when aspects of the computation are likely to reflect internal mental states, which may vary substantially even when external covariates remain constant, the relevant variables must be uncovered from neural data alone, most typically using a latent variable model [1][2][3][4][5][6].
Sentence 2: first, we extend Gaussian Process Factor Analysis (GPFA) [2], an algorithm that has been successfully applied in the context of extracting time-varying low-dimensional latent structure from binned neural population activity on single trials, to directly model the point-process structure of spiking activity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We then define the connecting module as a classifier, which takes the left and right phrases P (l) and P (r) as input and outputs a normalized score S(P (m) j | P (l) , P (r) , I) for each j ∈ {1, . . . , L}.
Sentence 2: conventional captioning methods usually encode the content of the given image into feature vectors, which are often difficult to interpret.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We use mIoU for semantic segmentation, error of per-pixel regression (normalized to image size) for instance segmentation, and disparity error for depth estimation.
Sentence 2: we also consider task-specific loss functions Although many hypothesis classes and loss functions have been proposed in the MTL literature, they generally yield the following empirical risk minimization formulation: for some static or dynamically computed weights c t per task, where Lt (✓ sh , ✓ t ) is the empirical loss of the task t, defined as Lt (✓ sh , ✓ t ) , 1 Although the weighted summation formulation (1) is intuitively appealing, it typically either requires an expensive grid search over various scalings or the use of a heuristic (Kendall et al., 2018;Chen et al., 2018).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our definition for equalized odds can be applied also to score functions: a score R satisfies equalized odds if R is independent of A given Y .
Sentence 2: this data is used to construct a (possibly randomized) predictor Ŷ (X) or Ŷ (X, A), and we also use such labeled data to test for non-discriminatory.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We compare the proposed method with the following baselines: (i) bag-of-words-based methods like TF-IDF [17] and LDA [8]; (ii) word/document embedding methods like Word2Vec [30], Glove [33], and Doc2Vec [27]; and (iii) the Wasserstein-distance-based method in [26].
Sentence 2: besides transfer learning, the idea of model distillation has been extended to control the learning process of neural networks [34,35,42].
Relationship: neutral
Domain: NeurIPS
Sentence 1: More closely related to our work is the Riemannian SVGD algorithm [18], which generalizes a gradient flow interpretation of SVGD [15] to Riemannian manifolds, and thus also exploits geometric information within the inference task.
Sentence 2: the SVGD algorithm then seeks a transport map T l+1 = I + Q that further decreases the KL divergence between (T l+1 ) * p l and π, for an appropriate choice of Q ∈ H d . the SVGD algorithm seeks a map Q ∈ H d such that where 0(x) = 0 denotes the zero map.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let I(a) = 1 when predicate a is true and I(a) = 0 otherwise.
Sentence 2: within this approach, we consider a prior distribution P over a space of classifiers that characterizes our prior belief about good classifiers (before the observation of the data) and a posterior distribution Q (over the same space of classifiers) that takes into account the additional information provided by the training data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With n u = 3n l , the model considerably improves upon the one discarding unlabeled data.
Sentence 2: the diagnosis models behave well, and the minimum entropy algorithm is not distracted by the two clusters; its performance is nearly identical to the one of training with labeled data only (cross-validation provides λ values close to zero), which can be regarded as the ultimate performance in this situation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: ( 4) is a fixed (loose) upper bound λ max (A) for all k. But in branch-and-bound search, any intermediate subproblem A m , with k ≤ m ≤ n, yields a new and tighter bound λ max (A m ) for the objective v * (k).
Sentence 2: finally, we note that even simple thresholding (ST), once enhanced with the variational renormalization, performs quite adequately despite its simplicity, as it captures at least 92% of the optimal variance, as seen in Figure 3(a).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For low-trace-norm learning, consider a sample S of size |S| ≤ Cn, for some constant C. Taking entries of Y to be of unit magnitude, we have Y S F = |S| ≤ √ Cn (recall that Y S is defined to be zero outside S).
Sentence 2: shifting the solid red (bottom) curve by this amount yields the dashed red (bottom) curve.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For comparison with the model by Yu and Ballard [4], we chose the files me03 and di06, each of which consisted of approximately ten minutes of interaction between a mother and a preverbal infant playing with objects found in a box of toys.
Sentence 2: the most parsimonious option according to the prior was not to learn any new words, but this did not account for the new evidence.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Section 2, we formally define coding cost, statistical typicality, and attentional focusing in face processing.
Sentence 2: these experiments show that a classical phenomenon known as the beauty-in-averageness (BiA) effect (see Figure 1a), whereby blends of multiple faces are usually found to be more attractive than the originals [10], can be suppressed or even reversed (termed Ugliness-in-Averageness or UiA), when the facial blends are created from recognizable faces [11] (see Figure 1d;e), or when attractiveness judgment of a mixed-race/mixed-gender blend is preceded by a racial/gender categorization task [12,13] (see Figure 2a;b), respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The size of joint representation C is the same with the rank K in lowrank bilinear pooling, C = K = 1, 024, but K 0 = K ⇥ 3 is used in the bilinear attention maps to increase a representational capacity for residual learning of attention.
Sentence 2: we evaluate on the VQA 2.0 dataset [1,8], which is improved from the previous version to emphasize visual understanding by reducing the answer bias in the dataset.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Furthermore, Q-learning in particular achieves higher accuracy models at a fraction of the computational cost of using all features, and is more effective than imitation learning.
Sentence 2: we have the following expression, where we use z(a) to indicate the a'th element of z: Note that in practice we can choose each f a to be a sparse vector such that f a • f a = 0 for all a = a; that is, each feature function f a "fills out" a complementary section of the feature vector f . A much more powerful approach is to create a feature vector as the composite of different extracted features for each vertex and edge in the model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show that this model can identify features that are location invariant by modeling a previous experiment on human feature learning.
Sentence 2: there were nine test images presented in a random order: Seen Both (an image in both training sets), Seen Unit (an image that only the unitized group saw), Seen Sep (an image only the separate group saw), New Unit (an image valid under the unitized feature set), New Sep (a image valid under separate feature set), and four other images that acted as controls (the images are under the horizontal axes of Figure 4).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure 3a shows how the number of edges varies versus the total number of active vertices for the multigraph, with different colors representing different random seeds.
Sentence 2: at a high level, this earlier model generates a weight measure W = i,j w ij δ (θi,θj ) (Caron and Fox [12] used, in particular, the outer product of a completely random measure), and the graph measure G is constructed by sampling g ij once given w ij for each pair i, j.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The rationale behind this scheme is that the initial model Â(0) is obtained essentially from an uninformed, ad hoc characterizer, for which one has to expect a large model variation and thus (on the average) a poor Â(0) .
Sentence 2: all computations were done in Matlab on 2 GHz PCs except the HMM training on dataset (d) which was done on a 330 MHz machine (the reported CPU times were scaled by 330/2000 to make them comparable with the other studies).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that by definition if C i is in the Markov blanket of C j , then C j is in the Markov blanket of C i .
Sentence 2: the marginal probability for each variable can be estimated by averaging the conditional marginals: Note that in Markov networks, P (X i |x The sampling distribution of Gibbs sampling converges to the posterior distribution (the distribution associated with the evidence instantiated Markov network) as the number of samples increases because the resulting Markov chain is guaranteed to be aperiodic and ergodic (see [15] for details).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure 2 (right plot) supports our claim that standard IRL is ineffective at learning rewards from misguided user demonstrations.
Sentence 2: 8 Acknowledgements We would like to thank Oleg Klimov for open-sourcing his implementation of the Lunar Lander game, which was originally developed by Atari in 1979, and inspired by the lunar modules built in the 1960s and 70s for the Apollo space program.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The advantage of this "greedy" homotopy path is that it provides a set of action-values that are a greedy fixed point for all settings of the L 1 regularization parameter.
Sentence 2: given a square matrix M and a vector q, a linear complementarity problem (LCP) seeks vectors w ≥ 0 and z ≥ 0 with w T z = 0 and w = q + Mz.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , z m ) of m examples, the task of a learning algorithm is to construct a classifier with the smallest possible risk without any information about D. To achieve this goal, the learner can compute the empirical risk R S (f ) of any given classifier f according to: We focus on learning algorithms that construct a conjunction of rays from a training set.
Sentence 2: r(B id ab ) ≤ 2R(G id ab ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: . .} along the relevant dimensions: P (spike|s) = P (spike)g(s 1 , s 2 , ..., s K ), If the inputs are Gaussian, the last requirement is not important, because relevant dimensions can be found without knowing a correct functional form for the nonlinear function g in Eq.
Sentence 2: in practice this involves finding a single relevant dimension first, and then iteratively increasing the number of relevant dimensions considered while adjusting the previously found relevant dimensions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We next consider the case, where A is an irreducible positive definite M-matrix.
Sentence 2: this raises the question whether the best known convergence rates of CCD in the literature are tight or whether there exist a class of problems for which CCD provably attains better convergence rates than the best known rates for RCD, a question which we will answer in Section 4.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This research is supported in part by NSF CISE Expeditions Award CCF-1139158, LBNL Award 7076018, and DARPA XData Award FA8750-12-2-0331, and gifts from Amazon Web Services, Google, SAP, The Thomas and Stacey Siebel Foundation, Apple, C3Energy, Cisco, Cloudera, EMC, Ericsson, Facebook, GameOnTalis, Guavus, HP, Huawei, Intel, Microsoft, NetApp, Pivotal, Splunk, Virdata, VMware, WANdisco, and Yahoo!.
Sentence 2: appendix B gives the formal details.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Before conducting intersections, a critical task is to (quickly) estimate the sizes of the intermediate results to plan the optimal intersection order [20,8,25].
Sentence 2: it is highly desirable to have a mechanism which can estimate join sizes very efficiently, especially for the lower-order (2-way and 3-way) intersections, which could potentially result in much larger intermediate results than higher-order intersections.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The live bonus heuristic encourages the agent to live longer so that it will potentially have a better chance of getting extrinsic rewards.
Sentence 2: the second baseline augmented the agent with a count-based bonus generated by the pixel-SimHash algorithm [Tang et al., 2017] (henceforth, A2C-pixel-SimHash baseline agent in short.)
Relationship: neutral
Domain: NeurIPS
Sentence 1: Acknowledgments This work is supported by US Army Research Office under contract W911NF-16-1-0265 and by the US National Science Foundation under grants CCF-1319140 and CCF-1718698.
Sentence 2: they show that the mean-squared error (MSE) of the estimation, together with a few other "order parameters", can be characterized as the solution of a deterministic system of coupled ordinary differential equations (ODEs) in the large system limit.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This, however, only applies whenever the empirical risk decomposes into individual loss terms (e.g.
Sentence 2: the current paper provides a) significantly improved performance bounds which match better what can be observed in practice and which apply to a wide range of regularization terms, b) a variant of the algorithm which does not require quadratic programming, yet enjoys the same fast rates of convergence, and c) experimental data comparing the speed of our solver to Pegasos and SVMPerf.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When there are multiple classes, this measures the closeness of the threshold for distinguishing the correct class out of the union of the rest of the classes (i.e., one-versus-rest).
Sentence 2: in this simple example, we can also see that the gradient magnitude is proportional to the difficulty because − w log(p(y i |x i , w)) = (1 − p(y i |x i , w)) x i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any subset S µ  This work was supported in part by NSF grants CMMI-1335155 and CNS-1161964, and by Army Research O ce MURI Award W911NF-11-1-0036.
Sentence 2: if ÷ AE 1/6, then any algorithm with success probability at least 2/3 requires at least min{¸/4, 1/48"} samples from the Unbiased Oracle.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given N (t) denoting the number of events occurred in the time interval [0, t) and τ t indicating the arrival times of the temporal events before t, the intensity for a time point t conditioned on the arrival times of all the previous events is defined as: It is worth noting that we do not consider edge effect in this paper, hence no events exist before time 0.
Sentence 2: unlike the SSMs, it lacks the capability of modelling events' latent states and their interactions.
Relationship: neutral