sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: In this section, we report the results of empirical studies comparing the algorithm we propose in Section 4 (referred to as Opt-D&S) with a variety of existing methods which are also based on the generative model of Dawid and Skene.
Sentence 2: the MV-D&S and the Opt-D&S algorithms consistently outperform the other methods in predicting the true label of items.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To address this dilemma, the ResNet paper's detection pipeline [10] inserts the RoI pooling layer into convolutions -this region-specific operation breaks down translation invariance, and the post-RoI convolutional layers are no longer translation-invariant when evaluated across different regions.
Sentence 2: with pre-computed region proposals, it is easy to end-to-end train the R-FCN architecture.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Second, the variance terms involved in Lepski's method are not completely explicit.
Sentence 2: using the Stoke's formula, ∆ is the unique linear operator satisfying Replacing the volume measure µ by a distribution P which is absolutely continuous with respect to µ , the weighted Laplace-Beltrami operator ∆ P is defined as where p is the density of P with respect to µ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is strictly worse than the complexity O( max{L 0 , M 2 /(2 )} 1/ ) of our approach.
Sentence 2: see Example 1 and Example 2 for details about the nonsmooth function f . We note that S-APG has been demonstrated with superior performance on both problems in [13], therefore we will only concentrate on comparing with it.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Markov random fields (MRFs) [12] have been applied to a wide variety of real-world problems.
Sentence 2: for example, the constraint satisfaction community has studied several special-purpose constraint types that can be solved more efficiently than using generic methods [4]; it would be interesting to explore whether these constraints arise within MRFs, and, if so, whether the special-purpose procedures can be integrated into the COMPOSE framework.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, if G 1 and G 2 are social networks, then k might capture to what extent their clustering structure, degree distribution, etc.
Sentence 2: writing the kernel explicitly in terms of A 1 and A 2 , we must have k(A 1 , A 2 ) = k(A 1 ,P A 2 P ) for any permutation matrix P . Permutation invariance has proved to be the central constraint around which much of the graph kernels literature is organized, effectively stipulating that graph kernels must be built out of graph invariants.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unfortunately, computing the gradients exactly seems very complicated for arbitrary parametrizations F θ , and we will focus our attention to mixture models of the form given in eq.
Sentence 2: while we could train a network θ : x → v ∈ R n to output per-pixel scores, it would be helpful, especially in domains with limited data, to bias the predictions by encoding some prior beliefs about the expected output.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In a first step, the learner applies to its input data S a fixed function ϕ : Examples Using the notations above, when S = X tr × {±1}, n = N , ϕ is the identity function and S is drawn i.i.d.
Sentence 2: we need a result on more general functions than sums of random variables, but which also takes into account the known dependency structure of the variables.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our method sets a new state-of-the-art IoU SegNet [28] 46.4 FCN-8 [29] 57.0 DeepLab-LFOV [24] 61.6 Bayesian SegNet [22] 63.1 Dilation8 [30] 65.3 Dilation8 + FSO [31] 66.1 DenseNet [20] 66.9 This work: on this dataset with mean intersection over union (IoU) score of 67.5%.
Sentence 2: these results show that aleatoric uncertainty is able to capture many aspects of this task which are inherently difficult.
Relationship: neutral
Domain: NeurIPS
Sentence 1: ( 11) for the "DIRECT 5-Mixture SGD" model which uses a mixture distribution with r 5 components, and t 3000 Monte Carlo samples for the entropy gradient estimator.
Sentence 2: while the Bayesian integrals that arise in GLMs can be easily computed in the case of conjugate priors, for general priors inference is challenging.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let I ⊂ {1, . . . n} be set of size n ′ < n. The subsampled loss Loss I will be computed only for the points k ′ ∈ I.
Sentence 2: if the weights are computed as in (1), it is easy to see that the loss function in (3) is the finite sample version of the squared L 2 distance between h and g 0 on the space of Riemannian metrics on M, w.r.t base measure πdV g0 Defining Loss for embeddings with s > d dimensions Consider G, G 0 ∈ R s×s , two symmetric matrices with G 0 semipositive definite of rank d < s. We would like to extend the G 0 norm of G to this case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our image representation is agnostic to any specific type of object detector; we take the "outsourcing" approach and assume the availability of these pre-trained detectors.
Sentence 2: while the OB representation offers a rich, high-level description of images, a key technical challenge due to this representation is the "curse of dimensionality", which is severe because of the size (i.e., number of objects) of the object bank and the dimensionality of the response vector for each object.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We will assume an infinite sequence of training data (x 1 , y 1 ), (x 2 , y 2 ), (x 3 , y 3 ), .
Sentence 2: finally it is worth noting that L ramp and L probit are meaningful for an arbitrary prediction space S, label space Y, and loss function L(y, s) between a label and a prediction.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our theoretical findings are complemented by empirical evidence which shows that our method delivers state-of-the-art performance.
Sentence 2: p can be described algebraically as All vertices of P lie on the hypercube {0, 1} n . We let x ⇤ denote the (unique) minimizer of f over P, and we let D denote the Euclidean diameter of P, namely, D = max x,y2P kx yk.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this respect, the two approaches may prove complementary, and it will be interesting to further consider their interrelations.
Sentence 2: we take three empirically motivated points as founding premises: (1) Neurons in dorsolateral prefrontal cortex represent action policies, (2) Neurons in orbitofrontal cortex represent rewards, and (3) Neural computation, across domains, can be appropriately understood as performing structured probabilistic inference.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This leads to the following approximate auxiliary function (based on the law of large numbers) which is merely the update rule for EM for θ n with s = 1, . . . , S virtual samples x m,s obtained from the m'th model p(x| θm ) for each of the other We now have an efficient update rule for latent variable models (mixtures, hidden Markov models, etc.)
Sentence 2: a large family of alternative information divergences exist to relate pairs of distributions (Topsoe, 1999) and are discussed in the Appendix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This value is too large for an exhaustive search.
Sentence 2: ( 1) is modified to become: For a probabilistic treatment with EM, we make a standard normal assumption of all distributions in form of: where 1 = [1, 1, .., 1] T . While this model is still identical to OLS, notice that in the graphical model, the regression coefficients b m are behind the fan-in to the outputs , we can view this new regression model as an EM problem and maximize the incomplete log likelihood log p(y|X) by maximizing the expected complete log likelihood log p(y, Z|X) : where Z denotes the N by d matrix of all z im .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The unnormalized graph Laplacian L of an undirected graph G has the following properties: (i) L is symmetric and positive semi-definite; (ii) the smallest eigenvalue of L is 0; (iii) L has n non-negative, real-valued eigenvalues 0 = λ 1 ≤ .
Sentence 2: we want to ascertain whether the effort of modeling the conditional independence structure of the overall network through the FRF formalism is justified by a suitable gain in prediction accuracy with respect to statistical models that do not focus explicitly on such dependence structure.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Developing methods to directly estimate the difference of two DAGs that do not share a topological order is of great interest for future work.
Sentence 2: to define these assumptions it is helpful to view (σ   v,w|S and σ w|S for all v, w, S. For consistency of the DCI algorithm we assume that the converse is true as well, namely that differences in B ij and σ j in the two distributions are not "cancelled out" by changes in other variables and result in differences in the regression coefficients and regression residual variances.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The value function u wv of an FSC P is the expected discounted sum of rewards for executing its policy P , and can be computed by solving a set of linear equations: Given an initial belief state B , an FSC's value at node Y is simply the expectation u ¤ HY rB D 5 B ¤ &¦ C u ¤ HY r¦ x ; the best starting node for a given B is determined by u ¤ §B D E u E¤ Y rB .
Sentence 2: many point-based algorithms including PBVI [12] (which is perhaps the best such algorithm) optimize the policy for a single initial belief state, capitalizing on a hopefully small reachable belief region.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In a highly volatile environment, one will be expected to have a high learning rate estimated by RL model, and a belief of low stationarity estimated by DBM.
Sentence 2: lose shift rate in all conditions (Fig 3b) have an inverted U shape as a function of alpha, where α = 0 leads to a random lose shift rate (1/3), and α = 1(fixed belief model) leads to the minimal lose shift rate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let n = 2 and consider RCD (Algorithm 3) with probabilities p 1 > 0 and p 2 > 0, p 1 + p 2 = 1.
Sentence 2: for every n ≥ 2 and T > 0, there exists A such that: (i) The rate of RCD with p i ∝ A ii is T times worse than the rate of RCD with uniform probabilities.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In addition, for ν = 1 the required scalar value λ B/0 is |r| here since V B ∩ V0 = {j, r} ∩ {r} = {r} noting that value λ B/0 is the same for ν = 2, 3.
Sentence 2: by alternating between Z 1 and Z 2 , we can maximise the log-likelihood iteratively; indeed this alternating maximisation is standard for solving matrix factorisation problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Consider a element-wise positive kernel matrix G standardized to be element-wise bounded 0  g i,j < 1 with unitary diagonal g i,i = 1 8 i 2 [n].
Sentence 2: in a question that asks to compare Proto and Criticism Condition and Proto Only Condition, a subject said that "The addition of criticisms made it easier to locate the defining features of the cluster within the prototypical images".
Relationship: neutral
Domain: NeurIPS
Sentence 1: When using the full learning rule for both features, the learning rate needs to be decreased until an agreeable signal-to-noise ratio between the drift introduced by the first term and the diffusion caused by the other terms is reached.
Sentence 2: an interesting alternative is that the trial mean is calculated by a prediction system, e.g., by topdown signals that use prior information or an internal world model to predict the expected value of the coding feature.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given a belief b, after executing a and receiving o, we can compute an updated belief b a,o using Bayes' theorem: b a,o (s) = kb(s) Pr(s |s, a) Pr(o|s a).
Sentence 2: in many realworld scenarios, planning can be simplified by decomposing the task into a hierarchy of smaller planning problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The present study mainly focuses on information processing at MSTd and VIP, where visual and vestibular cues are integrated/segregated to infer heading direction.
Sentence 2: when only cue x 2 is applied to module 2, the congruent neuronal network at module 1 receives a reciprocal input and generates a bump at x 2 , whereas the opposite neuronal network receives an offset reciprocal input and generates a bump at x 2 + π (Fig.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This allows a direct comparison of the algorithms proposed here with previously studied approximate 1-step greedy algorithms.
Sentence 2: namely, our bounds consist of concentrability coefficients C (1) , C (2) , C (2,k) and C π * (1) from [19,11], as well as two new coefficients C π * κ and C π * (1) κ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Furthermore, the risk functional can be simplified further by considering Our framework, on the other hand, alleviates the problem by minimizing the risk functional R µ (f ) = P ℓ(y, E P [f (x)]) dP(P, y) for f ∈ H with corresponding empirical risk functional the discussion at the end of Section 2).
Sentence 2: images of different scenes tends to generate distinct set of patches.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the first we show that whenever all f t 's are SLQC, there exists some t such that f t (x t ) − f t (x * ) ≤ .
Sentence 2: it is well known that quasi-convex optimization tasks can be solved by a series of convex feasibility problems [4]; generally solving such feasibility problems may be very costly [6].
Relationship: neutral
Domain: NeurIPS
Sentence 1: • -1.00 0 .00 1.00  This work was supported partly by the Human Brain Project grant P20 MH57180, the Danish Research councils for the Natural and Technical Sciences through the Danish Computational Neural Network Center (CONNECT) and the Technology Center Through Highly Oriented Research (THOR).
Sentence 2: ( 9) and that ul B_ j = 0 (since uluo = 0) we get ( 12) We note that this distribution is degenerate because the covariance is of rank N -l. For a sample Zj from the above distribution we have that UJ B_jB_;Uoz j = UJ B_jB_;UoUJ B_jB_; Xj = UJ B_jB_; Xj = Zj ( 13) As a second approximation, assume that the observed Zj are independent so that we can write the likelihood of A where we have used Eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is only weakly adaptive in the sense that only the stopping criterion for ML-RP is determined by monitoring the nature of the projected data.
Sentence 2: let Φ be a random orthoprojector Suppose M < N . Then, with probability exceeding 1 − ρ, the following statement holds: For every pair of points x, y ∈ M, and i ∈ {1, 2}, where d 1 (x, y) (respectively, d 2 (x, y)) stands for the geodesic (respectively, ℓ 2 ) distance between points x and y.
Relationship: neutral
Domain: NeurIPS
Sentence 1: But both the log determinant and the derivatives are needed for efficient GP marginal likelihood learning: the derivatives are required for gradient-based optimization, while the log determinant itself is needed for model comparison, comparisons between the likelihoods at local maximizers, and fast and effective choices of starting points and step sizes in a gradient-based optimization algorithm.
Sentence 2: a Python implementation of our approach is also available through the GPyTorch library: https://github.com/jrg365/gpytorch.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Performance varied continuously with thresholds for radial motions (φ=0, 180 o ) significantly lower than those for circular motions (φ=90,270 o ), (p<0.001; t(37)=3.39).
Sentence 2: where w ij is the strength of the recurrent connection between i th and j th units, (x i ,y i ) and (x j ,y j ) denote the spatial locations of their receptive field centers, σ Re (=10 o ) and σ Ri (=80 o ) together define the spatial extent of a difference-of-gaussians interaction between receptive field centers, and S R and S φ scale the connection strength.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This model was introduced in relation to DBM [7], inspired by related work showing that monkeys' choices when tracking reward biases that undergo change points are discounted in an approximately exponential fashion [2].
Sentence 2: the constant G t approximation is valid for arbitrary environments and does not depend on whether humans truly have mis-specified generative assumptions, as having been previously suggested [7,11,12].
Relationship: neutral
Domain: NeurIPS
Sentence 1: So we generically get slow logarithmic learning, consistent with the observations in [12].
Sentence 2: [4]) that the posterior mean for GP regression can be obtained as the function which minimizes the functional where f H is the RKHS norm corresponding to kernel k. (note that the GP framework gives much more than just this mean prediction, for example the predictive variance and the marginal likelihood p(y) of the data under the model.)
Relationship: neutral
Domain: NeurIPS
Sentence 1: Simulation results over ten independent runs are summarized in Figure 5.
Sentence 2: using Bayes' rule, the posterior distribution P (x * |{y t }, {x t }) can be rewritten as Since this posterior is equal to (6), one concludes (using ( 5)) that Note that this expression corresponds to the joint P (x * , {y t }|{x t }).
Relationship: neutral
Domain: NeurIPS
Sentence 1: An alternative approach is to view the problem as estimation of a stochastic model, combining a scoring metric on candidate graph structures with a goodness of fit measure to the data.
Sentence 2: our set-up includes the important situation in which the number of variables p may be large relative to the sample size n. we allow the graph  For many problems of interest, the graphical model provides a compact representation where the size of the neighborhoods are typically small-say d s p for all s ∈ V n . Our goal is to use 1 -regularized logistic regression to estimate these neighborhoods; for this paper, the actual values of the parameters θ ij is a secondary concern.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then it holds that Pr[lim t (x t , y t , x t−1 , y t−1 ) = (x * , y * , x * , y * )] = 0.
Sentence 2: a time indexed vector x at time t is denoted as x t . We denote by ∇ x f (x, y) the gradient of f with respect to variables in x (of dimension the same as x) and by ∇ 2 xy f the part of the Hessian in which the derivative of f is taken with respect to a variable in x and then a variable in y.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While we define the spectrum and mismatch feature maps without any reference to a generative model for the positive class of sequences, there is some similarity between the ¡ -spectrum feature map and the Fisher scores associated to an order ¡ Markov chain model.
Sentence 2: for two methods: the SAM-T98 iterative HMM, and the Fisher-SVM method.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Bayesian sequential updating or belief propagation, implemented in the form of particle filtering, has recently been used in estimating the hand trajectories of monkeys based on M1 neuron's responses [4] and the location of a rat based on the responses of the place cells in the hippocampus [3].
Sentence 2: at each time step of of decoding scheme, we can now filter a hypothesis particle (x 1 , x2 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: A column vector of ones of arbitrary dimension will be denoted by e. For A ∈ ℜ m×n and B ∈ ℜ n×k , the kernel K(A, B) maps ℜ m×n × ℜ n×k into ℜ m×k .
Sentence 2: in order to learn such a function we are provided with training data, A, containing S sets (or classes) of training samples: A = S j=1 (A j = {x j i } mj i=1 ), where the j-th set A j contains m j samples, so that we have a total of m = S j=1 m j samples in A.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is interesting to note that while using solely source training images yields very low accuracy (14.5% for SVM s ), adding even just a single labeled target image produces a significant improvement (TSVM achieves 18.5% accuracy with n t = 1, and 27.1% with n t = 5): this indicates that the method can indeed adapt the classifier to work effectively on the target domain given a small amount of strongly-labeled data.
Sentence 2: we note that in work concurrent to our own, Saenko et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This improvement is even maintained over TNN-RPCA and MC which require prior knowledge such as the true rank and exact outlier locations respectively.
Sentence 2: on the surface it may appear that the PB-RPCA objective (14) represents a rather circuitous route to solving (1), with no obvious advantage over the convex PCP relaxation from (3), or any other approach for that matter.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the graphon W is piecewise Lipschitz, Algorithm 1 is a consistent estimator of the graphon cluster tree of W. We have presented a consistency framework for clustering in the graphon model and demonstrated that a practical clustering algorithm is consistent.
Sentence 2: darker shades correspond to higher values of W. Figure 1b depicts a graphon W φ which is weakly isomorphic to W. W φ is the relabeling of W by the measure preserving transformation φ(x) = 2x mod 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We denote E[f (x k ) − f (x * )] by V k , and we use W k to denote the last expression in (23).
Sentence 2: we ran Acc-Prox-SVRG using values of η from the range {0.01, 0.05, 0.1, 0.5, 1.0, 5.0, 10.0}, and we chose the best η in each mini-batch setting.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Verbal fluency for two semantic categories, animals and foods, was administered in the last two testing rounds (2005 and 2010), yielding a total of 4714 lists for animals and 4624 lists for foods collected from a total of 5674 participants ranging in age from their early-60's to mid-70's.
Sentence 2: furthermore, FE cannot estimate the transition probabilities from an item that does not appear as the first item in the lists, which is common in real-world data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Gridworld, it is interesting to see that Φ good and Φ opt are quantitatively very similar, yet both have similar effects on the rate of convergence in the tabular case, whereas Φ opt considerably outperforms Φ good in the deep learning case.
Sentence 2: one reason for doing so is that expert demonstrations or advice can often be biased or incomplete, so being able to identify good advice from bad is critical to guarantee robustness of convergence.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each study 2 , i, we divided the MR images into D L i , D U i , and D S i , where an MR image (a.k.a slice) has three modalities available -T1, T2, and T1 contrast.
Sentence 2: considering the fact that MR images contain much noise and the three modalities are not consistent among slices of the same patient, our improvement is considerable.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Under the above assumptions and definitions, assume that the sequence of true random vectors x 0 and denoisers g 1 (r 1 , γ 1 ) satisfy Assumption 1.
Sentence 2: for illustration, we repeated the previous experiment, but A constructed using the SVD A = UDiag(s)V T with Haar distributed U and V and geometrically spaced s. Also, to make the problem more difficult, we set b 1 = 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let Ω sample the observed entires of Ã so that A1 through A3 hold.
Sentence 2: corollary 7 in the appendix can be used to establish the above conditions are necessary to recover A from a set of its principal submatrices which can be aligned in a overlapping sequence (e.g., submatrices running down the diagonal of A), which might be encountered when constructing a covariance matrix from sequentially sampled subgroups of variables.
Relationship: neutral