sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Notice that λ K and σ are eigengaps in HPFM model and PFM model respectively and depend only on the preference frame, and likewise for g row .
Sentence 2: the clustering C would not accurately capture the cluster structure of the matrix P . Hence, condition (3) amounts to requiring that no other cluster structure is present, in other words that within each block, the Markov chain induced by P mixes well.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now, the expected utility to agent i when it reports type θi , substituting for the payment term We can ignore the final term because it does not depend on the choice of θi at all.
Sentence 2: the online auction work considers a much simpler setting (see also [4]), for instance the allocation of a fixed number of identical goods, and places less emphasis on temporal strategies or allocative efficiency.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Whenever lim m→∞ ǫ(δ, m) = 0 the gap between the upper and lower bounds in Theorems 1 and 2 approaches R(ŷ) − min q R(q) as m → ∞ (ignoring constant factors).
Sentence 2: our first set of experiments involved two binary classification data sets that belong to a benchmark suite 1 accompanying a widely-used semi-supervied learning book [1]: the Columbia object image library (COIL) [17], and a data set of EEG scans of a human subject connected to a brain-computer interface (BCI) [18].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Second, we checked the sample efficiency of our algorithm by reducing the number of state-action pairs used for each training iteration from 50000 to 1000 for Hopper-v1, Walker2d-v1, HalfCheetah-v1 and to 5000 for other much high-dimensional tasks.
Sentence 2: this gives us a hint that a robust discriminator is an important factor in improving the sample efficiency of generative-adversarial approaches to imitation learning.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (1) allows learning of the stochastic transitions between reward functions (specifically, by learning !
Sentence 2: to extend such a partitioning to work for trajectories traversing through any (possibly unvisited) region of the state space, we propose using a generalized linear model to represent and predict the stochastic transitions between reward functions at any state (i.e., including states not visited in the expert's demonstrated trajectories) by exploiting features that influence these transitions (Section 2).
Relationship: neutral
Domain: NeurIPS
Sentence 1: For instance, the first two synergies shown in figure 3 were seen in all sets of synergies, from ¡ to ¤ .
Sentence 2: using these synergies, 50 episodes of duration 30 time steps were generated by scaling each synergy ¡ ¢ ¥¤ §¦ with random coefficients © and shifting it by random delays ¤ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, up to first order, matrix Then, to the extent that the above approximation holds, we can write: 5 Now, y t v k−1 x t is the margin of the (first-order) Perceptron vector v k−1 over a mistaken trial for the Higher-order Perceptron vector w k−1 .
Sentence 2: the same analysis also suggests a simple (but principled) way of switching on the fly between higher-order and first-order updates.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The above result clearly implies that for a probability measure ν on K, TV(δ 0 P t , νP t ) ≤ .
Sentence 2: itô's formula then gives , ν t ≥ 0 on the support of L, and ∇g(X t − X t ), ν t ≤ 0 on the support of L . Moreover ∇ 2 g(X t − X t ) = 1 |Xt−Yt| P (Xt−Yt) ⊥ where P x ⊥ denotes the orthogonal projection on x ⊥ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: If an attacker can associate a pseudonym with a human identity, the attacker may learn the user's transaction history.
Sentence 2: that satisfies is a constant that depends only on degree d, and I 1/2 (a, b) is the regularized incomplete Beta function, i.e., the probability a Beta random variable with parameters a and b takes a value in [0, 1 2 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Viewing n as an asymptotic parameter and γ as a fixed constant, we have  1)) , which holds for 0 < α < 1 2 , we see that any setting of γ such that α is bounded above zero by a constant gives an exponential gap between the error rate of PickyAdaBoost (which is (1/2−γ) n ) and the lower bound on AdaBoost's error provided by (7).
Sentence 2: to simplify the exposition, we have assumed that POPBM can exactly determine quantities such as Z t and the accuracies of the weak hypotheses.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is specifically of great interest for the neurodegenerative disease diagnosis, where the features from different regions of the brain are extracted, but not all the regions are associated with a certain disease.
Sentence 2: in the training stage, they denoise the feature values using a strategy similar to robust principle component analysis (RPCA) [7] and build the above LS-LDA model using the de-noised data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Barry and Hartigan [10,11] used product partition models as distributions over possible segmentations of time-series data.
Sentence 2: it seems that each learner reaches the boundary of its favored range of reactivity or stability when further changes in that direction cause it to either be so reactive that it often assigns relatively high probability of drift to many time steps for which there was no drift, or so stable that it cannot react to actual drift.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In contrast to previous work, we provide guarantees on the quality of the approximation as n increases.
Sentence 2: we define the n-inverse covering radius of compact K ⇢ X as the value ✏ n (K) = inf{✏ > 0 : N ✏ (K)  n}, when n is large enough so the infimum exists.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Basically, if the parameter ✓ could be included into the grid ⇥ 0 , Theorem 2.1 would turn into a bound on the regret R T (✓) with respect to ✓.
Sentence 2: in the adversarial setting, we develop an algorithm BOA+ whose cumulative excess risks is controlled by several bounds with different trade-offs between sparsity and rate for strongly convex loss functions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We conclude by noting that while the transition point from the early stage to the late stage for Q-ThS is near optimal in the heavily loaded regime, it does not yield optimal regret performance in the early stage in general.
Sentence 2: after a critical point when the algorithm has learned the system parameters well enough to stabilize the queue, the queue-length goes through regenerative cycles as the queue become empty.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any u × v matrix M we note M i,j its (i, j)-th entry.
Sentence 2: none of these methods is applicable directly to the p > 1 setting since they all rely on specific properties of the p = 1 case, such as the fact that the solution is piecewise-affine in λ and that the set of change-points is monotically decreasing with λ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With this notation, we have by the triangle inequality and Jensen's inequality that The bound (7) shows that solving the empirical minimization problem to accuracy sufficient to have guarantees the same convergence rates provided by Theorem 1.
Sentence 2: our second contribution is to develop a novel extension of simple averaging; it is based on an appropriate form of bootstrap [6,7], which we refer to bootstrap average mixture (BAVGM) approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: [14] show how SINR-optimal demixing can be approximated with extra sensors when assuming a white additive noise, and Koldovskỳ and Tichavskỳ [16] discuss how to achieve asymptotically low bias ICA demixing assuming white noise within a fixed ICA model.
Sentence 2: despite the significant work on noisy ICA algorithms, they remain less efficient, more specialized, or less practical than the most popular noise free ICA algorithms.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , w y sy ∈ R d . 6 Let s = � n y=1 s y , and let , where b yj is 1 if the j-th column of A came from {w y 1 , .
Sentence 2: now Q 0-1 1 can be written as , where e n−1 , e n denote the (n − 1) × 1 and n × 1 all ones vectors, respectively, and I n−1 denotes the (n − 1) × (n − 1) identity matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the parameters k, ⌘, and are chosen such that 12k⌘d  then .
Sentence 2: ( 3), with the perturbation matrix A t set to (r 2 R(x t )) 1/2 , the root of the inverse Hessian of R at the point x t . the distribution of y t is supported on the Dikin ellipsoid centered at x t , scaled by .
Relationship: neutral
Domain: NeurIPS
Sentence 1: To speed up convergence of SVM-Rank, we do not include rank constraints for memorability scores that lie within 0.001 of each other.
Sentence 2: we can compute the expected distance E(D j |v j ) of an image as: This represents the expected number of modifications in v from 1 to 0 (α) or from 0 to 1 (β).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now, it can be checked that for a, b ∈ A, we have L(V, a)/ L(V, b) = i∈{2,...,m} (p i /p 1 ) SC APP (b)−SC APP (a) .
Sentence 2: but this low-cost, large-scale data may require compromising quality: the workers are often unqualified or unwilling to make an effort, leading to a high level of noise in their submitted labels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Calculating a best response to a fixed strategy is computationally cheap (in games of perfect recall), costing only a single traversal of the game tree.
Sentence 2: we could (in principle) store Player 2's strategy for each iteration between t+1 and t+1000, and on iteration t+1000 calculate a best response to each of them and announce that Player 1 played those best responses following action a on iterations t + 1 to t + 1000 (and update the regrets to match this).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We note that near optimality of our algorithm does not depend on convexity property, or tree-like structure as many of the previous works; but only relies on geometry of the graphical structure which is present in many graphical models of interest such as those arising in image processing, wireless networks, etc.
Sentence 2: equivalently, from the optimization point of view, we wish to find an optimal assignment of the problem maximize H(x) where For completeness and simplicity of exposition, we assume that the function H is finite valued over Σ n . results of this paper extend for hard constrained problems such as the hardcore or independent set model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Section 3 we show that by making use of the "kernel trick" we are able to compute the sample covariance matrix in feature space in linear time in the number of samples.
Sentence 2: we tested all three algorithms on a very simple generative model on 3 binary nodes, where nodes ¥ through 3 % ¥ point to node 3 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Instead of requiring relevance labels, we use the pseudoinverse estimator to convert page-level reward into per-slot reward components-the estimates of φ x (j, a)-and these become targets for regression.
Sentence 2: both PI-OPT and SUP train gradient boosted regression trees (with 1000 trees, each with up to 70 leaves).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Making the story even more complicated, this taste-dependent rewarding value of food is demonstrated to be modulated by not only the approximated nutritional content of the food, but also the internal physiological state of the animal [16].
Sentence 2: "Reinforcement learning" and "negative-feedback models of homeostatic regulation" are two control theory-based computational frameworks that have had major contributions in learning and motivation literatures in behavioral psychology, respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The updates described before using GMM, the Kullback-Leibler divergence or the variance, all fit within the framework of empirical risk minimization, given by (6), which rewritten at the sample scale gives The proof follows from a standard approach from M -estimation theory [31, Theorem 5.7] but a particular attention shall be payed to the uniform law of large numbers because of the missing i.i.d.
Sentence 2: the importance sampling estimate of ϕ based on the sampling policy q, is given by where (x 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is ideal: our method is capable of near perfect recovery of the underlying social network over which a relatively small number of contagions diffused.
Sentence 2: we consider a diffusion process where a contagion (e.g., disease, information, product adoption) spreads over the edges of the network, and all that we observe are the infection times of nodes, but not who infected whom i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: On the other hand, if and ˜ are dependent, the expected value of on the boundaries of ˜ are not necessarily different.
Sentence 2: as stated earlier, according to PIC, 2 C|; = 2 C is independent form ( E|C , 2 E|C ) = (a, 2 E ), while as we can see from the expressions in (2), such independence does not hold in general in the reverse direction.
Relationship: neutral
Domain: NeurIPS
Sentence 1: However, marginalization of nuisance variables is potentially expensive and can mar the very sparsity of the graphical model that permitted efficient inference.
Sentence 2: proposition 7 can be used at runtime to determine what percentage δ R ( Ā, R) of the optimal objective is guaranteed, for any focused selector, despite the lack of conditional independence of S conditioned on R. In order to compute the bound, a greedy heuristic running on a separate, surrogate problem with R as the relevant set is required.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this area, most past work focuses on using exact (combinatorial) solvers to verify the robustness properties of networks, either via Satisfiability Modulo Theories (SMT) solvers [Huang et al., 2017, Ehlers, 2017, Carlini and Wagner, 2017 or integer programming approaches [Lomuscio and Maganti, 2017, Tjeng and Tedrake, 2017, Cheng et al., 2017.
Sentence 2: due to the skip connections, the indicator functions are not independent, so we cannot directly conjugate each individual indicator function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Minimality is natural with respect to our motivating applications-it is reasonable to assume that the measured nodes are non-redundant, in the sense that omitting a node from C would cause at least one edge to be lost from the measured communication pattern.
Sentence 2: propositions 1 and 2 show that even if the planted cover is not minimal, we can still recover its nodes with such unions of minimal vertex covers.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is in fact the same adaptiveness that leads to low regret that also leads to the strong revenue loss guarantees for adaptive learning algorithms.
Sentence 2: advertiser 1 can increase its own utility by bidding some b 1 smaller than v 1 but still large enough to ensure that b 1 ρ 1 (b 1 ) still be ranked the highest at the end of the learning stage.
Relationship: neutral
Domain: NeurIPS
Sentence 1: By decomposing the model parameter of each task into a product of two components: the across-task feature indicator and task-specific parameters, and applying different regularizers to the two components, we can select features for individual tasks and also search for the shared features among tasks.
Sentence 2: when many or all features are relevant to the given tasks, it may prefer the 2 norm penalty on c. only a limited number of features are shared between tasks, i.e., the features used by individual tasks are sparse with respect to the features selected as useful across tasks by c. We can impose the 1 norm penalty on β.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To examine if learning rate can be used to explain different types of learning behavior, we have simulated three types of behavior (No Learning, Expert and WSLS, Fig 1b ) in a low volatility condition.
Sentence 2: to examine the underlying computational principles that guide different learning behavior in an uncertain environment, we compared an R-W model and a Bayesian approach in a visual search task with different volatility levels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The discussion so far has been related to the characteristic property of k that makes γ k a metric on P. We have seen that this characteristic property is of prime importance both in distribution testing, and to ensure classifiability of dissimilar distributions in the RKHS.
Sentence 2: if constant functions are included in H, then it is easy to show that the characteristic property of k is also sufficient to achieve the Bayes risk.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With mixed proportion φ , successes of arm 1 and failures of arm 2 are attributed to successes on the shared "hidden" arm 3, whereas failures of arm 1 and successes of arm 2 are attributed to failures of arm 3.
Sentence 2: an agent learning a coupling parameter while sampling arms can manifest a range of exploratory behaviors that depend critically on both the recent reward history and the current state of the belief about c, illustrated in figure 3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We us the same training, validation and testing split as in [35].
Sentence 2: for example, by constraining y 1 to {0, . . . , y 1,max /2} and {y 1,max /2 + 1, . . . , y 1,max } for Ŷ1 and Ŷ2 respectively, while keeping all the other intervals unchanged.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In past work, we modeled forced-choice tasks using a response pathway with only the alternatives under consideration.
Sentence 2: of critical interest is the finding that a nonword prime formed by recombining two pleasant targets (e.g., HULIP from HUMOR and TULIP) or unpleasant targets (e.g., BIUT from BILE and SMUT) also served to bias the targets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The analysis is based on the assumption that the low frequency spectrum of voiced speech can be modeled as a sum of (noisy) sinusoids occurring at integer multiples of the fundamental frequency, f 0 .
Sentence 2: the output of the filterbank will consist of a sinusoid at f 0 and three other signals that are random or periodic, but definitely not sinusoidal.
Relationship: neutral
Domain: NeurIPS
Sentence 1: One consequence of the lower bound (19) is the existence of extremely badly conditioned instances, say with  = (100d) 2 and K = 3/2, such that in the first d 1 iterations it is impossible to decrease the initial error by more than a factor of 2 (the initial error may be chosen arbitrarily large as well).
Sentence 2: k. This means the "norm error" vanishes, while the "convex error" cannot increase too much, as A min z t ⇡ A min u min = 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This paper considers the problem of MV-set estimation using a training sample drawn from P , which in most practical settings is the only information one has about P . The specifications to the estimation process are the significance level α, the reference measure µ, and a collection of candidate sets G. All proofs, as well as additional results and discussion, may be found in [6] .
Sentence 2: the sample size will grow no faster than a polynomial in 1/ and 1/δ, paralleling results for classification.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We measure the proximity of a covariate vector x i ∈ R V +1 to β k using the softplus function of their inner product as ln(1 + e β k xi ), which is a smoothed version of ReLU(β k x i ) = max(0, β k x i ) that is widely used in deep neural networks [14][15][16][17].
Sentence 2: as x i moves away from hyperplane k, that proximity measure monotonically increases on one side of the hyperplane while decreasing on the other.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each of the 1000 classes, we train a linear SVM using all examples of that class available in the ILSVRC2010 training set (this number varies from a minimum of 619 to a maximum of 3047, depending on the class) and 4995 negative examples obtained by sampling five images from each of the other classes.
Sentence 2: as this procedure is performed identically for every image we consider, we will drop the dependence on I and simply refer to the "image" x.
Relationship: neutral
Domain: NeurIPS
Sentence 1: YKN acknowledges support from NRF/MSIT-2017R1E1A1A03070945, BK21Plus in Korea, MS from KAK-ENHI 17H01760 in Japan, KEK from IITP/MSIT 2017-0-01778 in Korea, FCP from BK21Plus, MITIP-10048320 in Korea, and DDL from the NSF, ONR, ARL, AFOSR, DOT, DARPA in US.
Sentence 2: lLR asymptotically produces the bias of Eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To address the above-mentioned issue, we extend the Rademacher random variables to the complex domain and consider all roots of z m = 1, that is, Ω = {ω j } m−1 j=0 where ω j = e i 2πj m . Suppose σ(i) is a Rademacher random variable with Pr[σ(i) = ω i ] = 1/m.
Sentence 2: for an n × n × n tensor T and a vector u ∈ R n , we define two forms of tensor products (contractions) as follows: Note that T(u, u, u) ∈ R and T(I, u, u) ∈ R n . For two complex tensors A, B of the same order and dimension, its inner product is defined as A, B := l A l B l , where l ranges over all tuples that index the tensors.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We have proposed a "rational process" model of perceptual multistability based on the idea that humans approximate the posterior distribution over the hidden causes of their visual input with a set of samples.
Sentence 2: the visual system might be able to evaluate only relative probabilities of two similar hypotheses (as in Metropolis-Hastings), or to compute local conditional posteriors of one scene variable conditioned on its neighbors (as in Gibbs sampling).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In such a case, overall clustering algorithm can be formulated in two steps: (i) performing principal component analysis (PCA) (Pearson, 1901) on the covariance matrix and (ii) recovering cluster membership matrix using the k eigenvectors that correspond to the k largest eigenvalues.
Sentence 2: the blockdiagonal structure of the Hessian matrix in (OPT8) can be exploited to solve this problem much more efficiently.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, there exists a constant C V ∈ R such that ∀ε > 0, Note that, while we require no assumptions on the densities here, in certain specific applications, such us for some Rényi-α quantities, where f = log, assumptions such as lower bounds on the density may be needed to ensure f is Lipschitz on its domain.
Sentence 2: in our framework, we assume that the underlying distributions are not given explicitly.
Relationship: neutral
Domain: NeurIPS
Sentence 1: On NORB, the model size used by Salakhutdinov and Hinton [18] is already as large as we are able to fit on most of our graphics cards, so we were not able to do the same for this dataset.
Sentence 2: we are able to classify nearly as well using a single large DBM and a generic inference procedure, rather than using a DBM followed by an entirely separate MLP model specialized for classification.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure (4) shows two images of roads in rural scenes and two fields.
Sentence 2: we demonstrate results for : (I) indoor and outdoor scenes (as reported in [2]), (II) rural English road scenes, (III) rural English fields, (IV) a painting of the French countryside, (V) a field of broccoli in the American mid-west, (VI) the Ames room, and (VII) ruins of the Parthenon (in Athens).
Relationship: neutral