sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: We start with the observation that the most natural formulation of averagecost ALP, which follows immediately from taking limits in the discounted-cost formulation and can be found, for instance, in [1,2,4,10], can be interpreted as an algorithm for approximating of the optimal average cost.
Sentence 2: to obtain a good policy, one needs a good approximation to the differential cost function.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For point loss functions, the instantaneous penalty L t (•) is encoded using a data point (x t , y t ) ∈ R d × {−1, 1} as L t (w) = P (x t , y t , w).
Sentence 2: for (surrogates of) non-decomposable loss functions such as pAUC and Prec @k the definition of instantaneous penalty itself is not clear and remains a challenge.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Using a scale sensitive losses, such as the cross entropy loss, does address this issue (if the outputs are scaled down toward zero, the loss becomes trivially bad), and one can obtain generalization guarantees in terms of norm and the cross entropy loss.
Sentence 2: we should be careful when comparing the norms of different models learned by minimizing the cross entropy loss, in particular when the training error goes to zero.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A classical example of this is a concern that any metric used to regulate financial risk may become invalid as soon as it is widely used, because actors in the financial market may attempt to game the metric to avoid regulation [14].
Sentence 2: much of the work on model feedback in fields like finance, education, or macro-economic theory has focused on negative results: there is an emphasis on understanding when feedback can happen and promoting awareness about how feedback can interact with policy decisions, but there does not appear to be much focus on actually fitting feedback.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The Euclidean version of (1) where M = R d and g is the Euclidean inner-product has been the subject of intense algorithmic development in machine learning and optimization, starting with the classical work of Robbins and Monro [26] to the recent spate of work on variance reduction [10; 18; 20; 25; 28].
Sentence 2: when (M, g) is a nonlinear Riemannian manifold, much less is known beyond [7; 38].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then, Ω(f ) can be the norm of a Reproducing Kernel Hilbert Space (RKHS), which means that there exist an Hilbert space H and a kernel function k : The reason for using an RKHS norm is the so-called representer theorem [5]: the function minimizing the corresponding regularized loss can be expressed as a linear combination of the kernel function evaluated at the labeled points.
Sentence 2: it is not straightforward to find the kernel associated with an RKHS norm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Learning a representation which can predict future video without labels has applications in action recognition and prediction and, when conditioned on the action of the agent, amounts to learning a predictive model that can then be used for planning and decision making.
Sentence 2: learning to predict physical phenomena poses many challenges, since real-world physical interactions tend to be complex and stochastic, and learning from raw video requires handling the high dimensionality of image pixels and the partial observability of object motion from videos.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In many cases, the maximum of a concave surrogate function can only be solved using other convex solvers and as a result the efficiency of the CCCP highly depends on the choice of the convex solvers.
Sentence 2: we show that by a suitable transformation of the network we can compute the maximum of the concave surrogate in closed form in time that is linear in the network size, which leads to a very efficient  ) ⇥ fv j (w (k) ) 4 Experiments We conduct experiments on 20 benchmark data sets from various domains to compare and evaluate the convergence performance of the four algorithms: PGD, EG, SMA and CCCP (EM).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For any sample (s, ā, ō, r, s ), the naive form would be The action ō is the minimizing opponent's action in computing π(s ).
Sentence 2: unfortunately, the number of terms in the summation within the first update equation is exponential in N . the vector φ(s, ā, ō) − γ ā ∈ Ā π(s , ā )φ(s , ā , ō ) can be computed on a component-by-component basis avoiding this exponential blowup.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Blei et al do not address the specific problem considered here, of using both page structure and hyperlink structure in web page classification.
Sentence 2: they do apply their technique to two closely related problems: they augment a page classification method with local features based on the page's URL, and also augment content-based classification of "text nodes" (specific substrings of a web page) with page-structure-based local features.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Specifically, according to the MLE, Σ −1 is estimated by solving the optimization problem which is obtained by applying − log to the probability density function of the Normal distribution.
Sentence 2: if the number of samples is lower than the dimension of the vectors, i.e., m < n, then S in (1) is rank deficient and not invertible, whereas the true Σ is assumed to be positive definite, hence full-rank.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Typically the optimal ρ is in the order of KL( ŵX dπ||dπ)/n, and hence the rate of convergence given on the right-hand side is no better than O( 1/n).
Sentence 2: the more interesting case is when there exists a constant b ≥ 0 such that This condition appears in the theoretical analysis of many statistical estimation problems, such as least squares regression, and when the loss function is non-negative (such as classification).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The former is an online algorithm specially designed to minimize the average rank in feeds sorted in reverse chronological order and the latter is an offline algorithm specially designed to maximize the time at the top in feeds sorted in reverse chronological order.
Sentence 2: because REDQUEEN assumes that the feed is inverse chronologically sorted and posts with intensity / rank chrono (t), we also compare our method TPPRL against a stronger heuristic RQ ⇤ , which posts with intensity / rank priority (t).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This shows that when the set of feasible actions is strongly convex, a directional hint can improve the regret bound beyond what has been known to be achievable by an approximation hint.
Sentence 2: we note that our results require the hints to be always valid, whereas the algorithm of Rakhlin and Sridharan [19] can adapt to the quality of the hints.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Although it is always desirable to invent an exact algorithm that could be mathematically proved to obtain a better scalability property, it is beneficial to demonstrate the value of larger number of variables with an industrial application.
Sentence 2: for a problem with billions of variables, there are existing practical approaches to reduce it into a smaller number of variables and then solve it with traditional approaches designed for centralized algorithm.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then for j ∈ A we have where (a) follows by using Lemma 5 to bound T j (n) ≤ τ ji when Z i < ∆ji .
Sentence 2: the total number of pulls for arms j for which Z i ≥ ∆ji /2 is at most n. (b) follows by bounding τ ji in expectation using Lemma 6.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Our SSL methods based on Ω H,p , p = 1, 2 outperform consistently the clique expansion technique of Zhou et al [11] on all datasets except 20newsgroups 3 .
Sentence 2: 20newsgroups is a very difficult dataset as only 10,267 out of the 16,242 data points are different which leads to a minimum possible error of 9.6%.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The Wasserstein distance is inherently based on a notion of distance between images which in all implementations of Wasserstein GANs (WGAN) so far has been the 2 distance.
Sentence 2: the imaging literature contains a wide range of metrics used to compare images [4] that each emphasize different features of interest, such as edges or to more accurately approximate human observer perception of the generated image.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: On the other hand, if the minimum step length τ is computed naively by Lemma 5, it takes O(n 2 |P|) computations, which could be a bottleneck of the algorithm.
Sentence 2: this bottleneck can be eased by introducing a working set approach: only a fixed number of constraints in the working set are evaluated at each step, while the working set is updated, say, every 100 steps.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: TD(λ) is known to converge when used with linear function approximators, if states are sampled according to the policy being evaluated -a scenario called onpolicy learning (Tsitsiklis & Van Roy, 1997).
Sentence 2: the absence of either of these requirements can cause the parameters of the function approximator to diverge when trained with TD methods (e.g., Baird, 1995;Tsitsiklis & Van Roy, 1997;Boyan & Moore, 1995).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: In cases where a bound u max on m t=1 A t F t is known, we can restrict t to [0, u max ] and discretize problem (8) over this interval.
Sentence 2: the conclusion of Lemma 2 does not hold for a finite horizon and we need to impose additional linear constraints y[t] ≤ y[t − 1] to ensure the monotonicity of y.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The top six eigenvalues of its gradient covariance matrix are well separated from the rest as seen in Figure 4(a).
Sentence 2: the function is far from smooth when projected onto the leading 1D or 2D active subspace, as Branin Franke Sine Norm Sixhump StyTang Hart3 SE 6.02e-3 8.73e-3 8.64e-3 6.44e-3 4.49e-3 1.30e-2 SKI 3.97e-3 5.51e-3 5.37e-3 5.11e-3 2.25e-3 8.59e-3 D-SE 1.83e-3 1.59e-3 3.33e-3 1.05e-3 1.00e-3 3.17e-3 D-SKI 1.03e-3 4.06e-4 1.32e-3 5.66e-4 5.22e-4 1.67e-3 Table 1: Relative RMSE error on 10000 testing points for test functions from [24], including five 2D functions (Branin, Franke, Sine Norm, Sixhump, and Styblinski-Tang) and the 3D Hartman function.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Our VPNs are related to Value Iteration Networks [35] (VINs) which perform value iteration (VI) by approximating the Bellman-update through a convolutional neural network (CNN).
Sentence 2: vINs perform VI over the entire state space, which in practice requires that 1) the state space is small and representable as a vector with each dimension corresponding to a separate state and 2) the states have a topology with local transition dynamics (e.g., 2D grid).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Given a (η, Φ)-mixable loss , we verify that Algorithm 3 is well defined; for simplicity, assume that dom = A and L is twice differentiable on ]0, +∞[ n . From the definition of an entropy, |Φ| < +∞ on ∆ k , and thus the entropic dual Φ t is defined and finite on all R k (in particular at θ t ).
Sentence 2: from Proposition In what follows, we focus on a particular instantiation of Algorithm 3 where we choose β t := −η t−1 s=1 ( x s (A s ) + v s ), for some (arbitrary for now) (v s ) ⊂ R k . The (v t ) vectors act as correction terms in the update step of the AGAA.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: That the majority of the components is positive stems from the fact that the underlying signals in calcium imaging are all made up of photons, and they elicit activity above a baseline as opposed to fluctuating around it.
Sentence 2: not all positive sources are cells that could be extracted by an algorithm (some could be neuropil, other noise, or non-captured cells); hence we model them as generic gross non-negative contamination sources.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This involves computing ∇g along all m = |Y| of its components, which may be intractable.
Sentence 2: for the 2 2 smoothing, the gradient ∇h µ 2 2 (z) is given by the projection of z/µ onto the simplex, which selects a small number, denoted K z/µ , of its largest coordinates.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then for any δ ∈ (0, 1), best-arm MAB algorithms can identify i with probability at least 1−δ based on at most 2 i =i ∆ −2 i log(1/δ) total samples (see the paper [9] for a brief survey and [10] for an application to clinical trials).
Sentence 2: if samples are allocated uniformly to the alternatives under the same conditions, then the most natural procedures require K max i =i ∆ −2 i log(K/δ) samples before returning i with probability at least 1 − δ.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The difference between RL's competition between multiple actions and SR's motivation of a single action might seem trivial, particularly if an extra, nUll, action is included in the action competition in RL, so the subject can actively choose to do nothing.
Sentence 2: there is substantial evidence from experi-ments in which drive states (eg hunger, thirst) are manipulated, that motivation in the SR sense works in a sophisticated, intrinsically goal-sensitive, way and can exert unexpected effects on instrumental conditioning.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: ( 8) implies that if we ignore the gradient of the noise component, z n j , the tendency of increasing the SNR of z j will attempt to increase the variance of the signal component, z s j , instead of increasing the feature correlation of the lower layer.
Sentence 2: we find in practice that such modification to the gradient causes optimization difficulties, preventing the training process from converging.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Building on this idea, algorithms have been proposed for answering queries on probabilistic Kripke structures [10] and on influence diagrams that define such structures [8].
Sentence 2: these algorithms have not addressed the fact that as agents interact with the world over time, the set of observation sequences they could have received (and possibly the set of beliefs they could arrive at) grows exponentially.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Although this modeling is indirect, recurrent networks nonetheless can achieve state-of-the-art results on many robotics [18,23], vision [34,50], and natural language tasks [15,20,38] when training succeeds.
Sentence 2: recurrent model optimization is hampered by two main difficulties: 1) non-convexity, and 2) the loss does not directly encourage the internal state to model the latent state.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A classic result of Kruskal [10] has been employed to prove the identifiability of a wide class of latent variable models, including hidden Markov models and certain restricted mixtures of latent tree models [11][12][13].
Sentence 2: these techniques cannot be directly applied to parsing models since the tree topology varies over an exponential set of possible topologies.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Several works characterize convergence of EM to stationary points of the log-likelihood objective under certain regularity conditions (Wu, 1983;Tseng, 2004;Vaida, 2005;Chrétien and Hero, 2008).
Sentence 2: these analyses do not distinguish between global maximizers and other stationary points (except, e.g., when the likelihood function is unimodal).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Because the precise mechanism by which neural responses generate hemodynamic responses is an active area of research [7], strong conclusions cannot be drawn based on simulated fMRI data alone.
Sentence 2: establishing "ground truth" validity for connections estimated by GC on fMRI data require concurrent, brain-wide invasive neurophysiological recordings during fMRI scans, a prohibitive enterprise.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: By appropriately tracking cross terms, these results can also be applied to more general (non-tetrahedral) polynomials in Gaussian random variables [23].
Sentence 2: our random process L(a, w) involves a nonlinear phase term ψ(Aw) which is not a polynomial, and hence is not amenable to a direct appeal to existing results.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: A common choice is the regression loss function i ( f (x i ) − c i ) 2 , which encourages the model to predict cost accurately.
Sentence 2: as we care only about the relative order of program run times rather than their absolute values in the selection process, we can instead use the following rank loss function [6]: We can use the prediction f (x) to select the top-performing implementations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This approach provides a unified framework for detection and post-processing (non-maximum suppression), and handles issues related to the object with variable aspect ratios naturally.
Sentence 2: object localization is an inherently difficult task due to the large amount of variations in objects and scenes, e.g., shape deformations, color variations, pose changes, occlusion, view point changes, background clutter, etc.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Furthermore, given observation Y l (t), assume that the transformation by (1) has modeling and measurement uncertainty in Gaussian distribution, i.e., where w stkt (t) is Gaussian with zero mean and variance Σ l stkt , i.e., N (•; 0, Σ l stkt ).
Sentence 2: thus, the likelihood of observation Y l (t) at state s t and mixture k t is Refereeing to (3) and ( 5), the posterior distribution of Θ(t) given Y l (t) is The time-varying noise parameter is estimated by MMSE, given as, it is difficult to obtain the posterior distribution p(Θ(t)|Y l (0 : t)) analytically, since p(µ l stkt (t), µ l n (t)|Y l (t)) is non-Gaussian in µ l stkt (t) and µ l n (t) due to the non-linearity in (4).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: If ε = 0, this is equivalent to the classical spatial scan statistic [1][2]: we are testing for regions where q in is greater than q out .
Sentence 2: in many real-world applications (including the epidemiological and fMRI datasets discussed later) we expect some fluctuation in the underlying baseline; thus, we do not want to detect all deviations from baseline, but only those where the amount of deviation is greater than some threshold.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Then, if we solve (5) with s = 8 r log p n and g = 8 then, with probability at least 1 c 1 exp( c 2 n 2 s ) c 3 /q 2 , we have the error bound: Let us briefly compare the result from Corollary 2 with those from single-structured regularized estimators.
Sentence 2: since the total sparsity of ✓ ⇤ is bounded by k✓k 0  ms g + s, "clean" `1 regularized least squares, with high probability, gives the bound [11]: the support of ✓ ⇤ also can be interpreted as comprising s g + s disjoint groups in the worst case, so that "clean" `1/`2 group regularization entails, with high probability, the bound [11]: (sg+s)m n + q (sg+s) log q n ◆ .
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For inference of average treatment effect, we see that at the low noise levels CEVAE does slightly worse than the other methods, with CEVAE nh = 0 doing noticeably worse.
Sentence 2: similar to the counterfactual case, CEVAE is significantly more robust to proxy noise, achieving quite a low error even when the direct proxies are completely useless at noise level 0.5.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: We note that these constraints can be removed by simply redefining U t (b t ) = ∞ ∀b t = b i t . A naive approach to minimizing (4) would take O(K T ) for K locations per frame.
Sentence 2: we can efficiently solve the above problem in O(T K 2 ) by using dynamic programming through a forward pass recursion [3]: By storing the pointers in (6), we are able to reconstruct the least cost path by backtracking from the last frame T . We note that we can further reduce this computation to O(T K) by applying distance transform speed ups to the pairwise term in (3) [11].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: To the best of our knowledge, we are the first to introduce the notion of entrywise PDFs for binary matrices and to develop implicit sampling techniques for computing them efficiently.
Sentence 2: our work is related to the problem of sampling from the space of binary matrices with fixed marginals, studied extensively in many domains [2,6,7,9,21], primarily due to its applications in statistical significance testing [14,17,20].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: 2 This motivated further development, including a recent actor-critic algorithm proven to converge when the critic uses linear function approximation [Maei, 2018], as well as several methods using the approximate off-policy gradient such as Deterministic Policy Gradient (DPG) [Silver et al., 2014, Lillicrap et al., 2015, ACER [Wang et al., 2016], and Interpolated Policy Gradient (IPG) [Gu et al., 2017].
Sentence 2: it remains an open question whether the foundational theorem that underlies these algorithms can be generalized beyond tabular representations.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: For the prediction of v t given v 1:t−1 , we (i) first obtain a sample from q φ (h of the current hidden state ; (iii) make a prediction for v t using p θ (v t |h 1:t , v 1:t−1 ).
Sentence 2: synthesizing samples is conceptually simper.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Including the entropy into the learning cost function can be seen as adding a regularizer that promotes a compressible representation of the network or feature representation.
Sentence 2: two major challenges arise when minimizing D + βR for DNNs: i) coping with the non-differentiability (due to quantization operations) of the cost function D + βR, and ii) obtaining an accurate and differentiable estimate of the entropy (i.e., R).
Relationship: contrasting
Domain: NeurIPS
Sentence 1: As with bandit problems, the states of the arms evolve independently given the actions taken, suggesting that there might be efficient algorithms for large-scale settings, based on calculating an index for each arm, which is a real number associated with the (belief-)state of that arm alone.
Sentence 2: while bandits always have an optimal index policy (select the arm with the largest index), it is known that no index policy can be optimal for some discrete-state restless bandits [17] and such problems are in general PSPACE-hard even to approximate to any non-trivial factor [10].
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Theorem 3.3 suggests that it is a good heuristic to include linear features in SVGD, because Gaussianlike distributions appear widely thanks to the central limit theorem and Bernstein-von Mises theorem, and the main goal of inference is often to estimate the mean and variance.
Sentence 2: the more commonly used Gaussian RBF kernel does not have similar exact recovery results for the mean and variance, even for Gaussian distributions.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: The primary contribution of this paper is a theoretical analysis that substantially relaxes the strength of this second assumption to just a form of "expansion" of the underlying distribution (a natural analog of the graph-theoretic notions of expansion and conductance) that we show in some sense is a necessary condition for co-training to succeed as well.
Sentence 2: we will need a fairly strong assumption on the learning algorithms: that the h i they produce are never "confident but wrong" (formally, the algorithms are able to learn from positive data only), though we give a heuristic analysis of the case when this does not hold.
Relationship: contrasting