sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: This approach introduces an interaction between G and our classifier that we do not fully understand yet, but empirically we find that optimizing G using feature matching GAN works very well for semi-supervised learning, while training G using GAN with minibatch discrimination does not work at all.
Sentence 2: semi-supervised learning with minibatch discrimination does not produce as good a classifier as does feature matching.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Because the number of values of α such that |α| ≤ p is r pd = C(p + d, d), the total complexity of the algorithm is where n c is the number of cluster centers that are within the cut-off radius of a target point.
Sentence 2: few sources have a contribution greater than q i ǫ at low bandwidths, since the cut-off radius becomes very small.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, if X p , X q , X r are any three observed nodes in T , then T |{X p , X q , X r } must have the configuration on the left panel of Figure 2.1, and it can be seen that ph T (π p , π q ) ∪ ph T (π q , π r ) = ph T (π p , π r ) for any permutation (π p , π q , π r ) of (p, q, r).
Sentence 2: now we present the polynomial characterization of a Gaussian latent tree graphical model that extends the results in Shiers et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Linear interpolation of the edge weights between the t i is used to smoothly add the new edges and gradually delete the ones to be deleted.
Sentence 2: under the constant-trace assumption, we construct an estimator for tr(B) For a time-varying trace tr(B(t)), use the time-averaged kernel In the future we will derive rates for the time varying case by choosing an optimal h. These estimators allow us to construct a sample covariance matrix for A: We (similarly to B(t)) apply the GLasso approach to Ã.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our results paint a bleak picture for the use of value-iteration-based algorithms for computing stationary equilibria.
Sentence 2: a NoSDE (pronounced "nasty") game is a deterministic turn-taking Markov game Γ with two players, two states, no more than two actions for either player in either state, and no deterministic stationary equilibrium policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: At each time t, given the history h t , the agent can compute the posterior distribution µ t given by µ t (Θ) = P(θ * ∈ Θ|h t ) for any set Θ.
Sentence 2: based on the key property of Lemma 2, we derive an upper bound on R 0 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: To reduce the computational complexity, Greengard and Strain proposed the Fast Gauss Transform (FGT) [5], using two expansions, the far-field Hermite expansion and the local Taylor expansion, and a translation process that converts between the two, yielding an overall complexity of O(M + N ).
Sentence 2: ǫ is modified every iteration) if we use inexact Krylov subspaces [23] for the conjugate gradient iterations.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to train the CAI model, we group θ into four categories -front, left, right and back, and provide it this information as a one-hot encoded vector.
Sentence 2: more notably, CAI performs significantly worse than our baseline models, indicating that the supervised approach of invariance induction can worsen performance with respect to nuisance factors not accounted for during training.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We then observe that Φ c−θ γ plays an analogous role in Equation 3 to w1 in (1).
Sentence 2: under G 1 the probability of E occurring (assuming b + ) is a similar noisy-AND-NOT parameterization can be used for preventive causes [4], but we focus on generative causes in this paper.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For both datasets, we preprocessed with a high-pass filter at 800 Hz using a fourth order Butterworth filter before we analyzed the time series.
Sentence 2: observe that making this decision involves marginalizing over all possible cluster assignments ⌫ t , and all values of the weight vector y t . having made this decision, we collapse these posterior distributions to point estimates b ⌫ t and b y t equal to their MAP values.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is achieved by exploiting adversarial domain classification in the resulting latent feature space.
Sentence 2: with the above discussions, we define the objective functions L adv Dx and L adv G for adversarial learning between image discriminator D x and generator G as: the objective function for domain classification is derived as: where l x denotes the domain prediction of image discriminator D x .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since we consider models where η = O(1) is a small constant, this implies that we have a polynomial sample complexity in p, d, r. The final step involves using the estimated pairwise marginals of each component { P spect (Y a , Y b |H = h)} to obtain tree approximation of the component via Chow-Liu algorithm [10].
Sentence 2: if we resort to operations over only low order statistics, we require additional conditions such as (8) for identifiability.
Relationship: neutral
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: as an alternative, Wilson and Nickisch [28] proposed the structured kernel interpolation (SKI) approximation, where U is a uniform grid of inducing points and W is an n-by-m matrix of interpolation weights; the authors of [28] use local cubic interpolation so that W is sparse.
Relationship: neutral
Domain: NeurIPS
Sentence 1: [2008], FASTSWAP uses a specific initial distribution at each round, applies the power method to a modification of the original stochastic matrix, and uses, as an approximation, an average of all the iterates at that round.
Sentence 2: theorem 3 implies that FASTTIMESELECTTRANSDUCE achieves the same timeselection swap regret guarantee as the algorithm of Khot and Ponnuswami [2008] but with a perround computational cost that is only in ), which is an exponential improvement!
Relationship: neutral
Domain: NeurIPS
Sentence 1: Nevertheless, we also report classification accuracy in Table 1 to show that a) the learned models have similar characteristics as earlier work, in particular to [29], where the an identical model was trained using structured SVM learning, and b) adaptive MMP can achieve as high prediction accuracy as ordinary Gibbs sampling, as long as the confidence parameter is not chosen overly optimistically.
Sentence 2: sequential sampling with the option of early stopping has a long tradition in Bayesian statistics.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , x n then we reduce it to MDP with n + 1 states,s 1 , .
Sentence 2: . . c T over actions A, the algorithm selects a distribution q t over A (using only the previous loss functions where c t (a) ≤ M . Furthermore, we also assume that decision distributions do not change quickly: These assumptions are satisfied by the multiplicative weights algorithms.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Such M ( w) is denoted M 0 ( w) in the following text.
Sentence 2: let W i,j,k denotes the set of all possible walks w satisfying s 1 =s i , s |w| =s j and s |w|+1 =s k . Then we have V (s i ) = w∈W i,j,k (γ |w|−1 (s t ,s t+1 ) on w p s t ,s t+1 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Following the same lookahead strategy as LSID3, we sample the space of trees under each candidate split.
Sentence 2: assume a problem with |C| classes and a misclassification cost matrix M . Let c be the class label in a leaf l. Let m be the total number of examples in l and m i be the number of examples in l that belong to class i.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Combining the last two inequalities we conclude that holds with probability at least 1 − 2e −n ∆ 2 8 − e − η 2 2 .
Sentence 2: for the loss in (1.1) the generalized gradient takes the form projected gradient descent takes the form where µ τ is the step size and K = {w ∈ R d ∶ R(w) ≤ R} is the constraint set with P K denoting the Euclidean projection onto this set.
Relationship: neutral
Domain: NeurIPS
Sentence 1: else false reward = s(1) + s(2) + s(3) AROLLOUT translates the RDDL code into algebraic expressions using standard transformations from a logical to a numerical representation.
Sentence 2: anytime algorithms are typically scored using the log of marginal probability; the score for solution Current state of the art exact algorithms use branch and bound techniques (e.g., [11]).
Relationship: neutral
Domain: NeurIPS
Sentence 1: When p 2 C, excluding [n] \ S will only reduce Z.
Sentence 2: for the class C = M d n of monotone distributions over [n] d we require an optimal ⇥ n d/2 /" 2 number of samples, where prior work requires ⌦ p n log n/" 6 samples for d = 1 and poly (1/") for d > 1 [6,7].
Relationship: neutral
Domain: NeurIPS
Sentence 1: See Figure 2 and the accompanying text in Appendix E for a plot of the points (⇢, log 10 ( )), where is the final average change in the messages at termination of the algorithm.
Sentence 2: we show that in the pairwise Bethe case, the polytope may be expressed geometrically as the convex hull of single-cycle forests formed by the edges of the graph.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To allow probability measures P without densities (i.e., P µ), we assume each basis element φ z : X → R is a bounded function, so that P z := EX∼P [φ z (X)] is well-defined.
Sentence 2: then, for any P ∈ F G , we define the implicit risk of X at P by R I (P, X) := E X1:n∼P (P, P X(X1:n,Z)|X1:n ) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: While these algorithms worked well in practice, until recently, little could be shown analytically about their performance.
Sentence 2: proof sketch: Using tail distributions of chi-squared random variables, it is shown that the minimum value for the correlation |a ′ j y| 2 when j ∈ I true is greater than the maximum correlation when j ∈ I true .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In SNE, the class posterior probabilities p(c k |x n ) are replaced by the probability p(x m |x n ) of object x n under a Gaussian distribution centered on x m . When the inputs (posterior probabilities) to PE come from an unsupervised mixture model, PE performs unsupervised dimensionality reduction just like SNE.
Sentence 2: 1 The computational complexity of PE is O(N K), which is much more efficient than that of pairwise (dis)similarity-based methods with O(N 2 ) computations (such as SNE, MDS, or Isomap).
Relationship: neutral
Domain: NeurIPS
Sentence 1: When β = 1, all tensor slices have equal Frobenius norm.
Sentence 2: there can only be o(n 2/3 ) slices j for which T j, * , * for each of them we can afford to take O(n 2 ) 2 -samples and still have an O(n 2+2/3 ) = o(n 3 ) sublinear running time.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let α j k and β j k be the sensitivity and specificity respectively of the j th annotator corresponding to the threshold k, that is, Hence each annotator is parameterized by a set of 2(K − 1) parameters [α j 2 , β j 2 , .
Sentence 2: if the true label is zero, the specificity (1−false positive rate) β j is defined as the probability that annotator labels it as zero.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Qualitatively, GP learning curves are relatively well understood for the scenario where the inputs x come from a continuous space, typically R n [3,4,5,6,7,8,9,10,11].
Sentence 2: in section 2 we give a brief overview of GP regression and summarize the approximation for the learning curves used in previous work [4,8,12].
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the negative training sets, we obtained noncoding RNAs other than pre-miRNAs and exonic regions of protein-coding genes from NCBI (http://www.ncbi.nlm.nih.gov), fRNAdb [23], NONCODE [24], and   snoRNA-LBME-db [26].
Sentence 2: reliable pre-miRNA identification requires features other than the secondary structure to be considered, since false positives may be generated due to the limitations of structure prediction algorithms and the inherent unpredictability of these structures [21].
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , w K ) ∈ R K . Note minimizing the cross-entropy loss is equivalent to maximizing the likelihood of , which is biased towards fitting neither the data with y i = 1 nor these with y i = 0, since NLL(x i ) = ln(e −yiw ln(1+e Bx i ) + e (1−yi)w ln(1+e Bx i ) ).
Sentence 2: it is straightforward to show that iSHM with a single unit-weighted hyperplane reduces to logistic regression To interpret the role of each individual support hyperplane when multiple non-negligibly weighted ones are inferred by iSHM, we analogize each β k to an expert of a committee that collectively make binary decisions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The form of (2) shows that DUDE is a sliding window denoiser with window size 2k + 1; namely, DUDE returns the same denoised symbol at all locations i's with the same value of z i+k i−k .
Sentence 2: it is clear that s cannot evaluate its loss since it does not know what x is, but the following shows an unbiased estimate of the expected true loss, which is only based on Z and s, can be derived.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Theorem 1 Given two simple, undirected graphs G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ), with combinatorial Laplacians L G1 and L G2 ,the combinatorial Laplacian of the Cartesian product graph G 1 × G 2 is then given by: Here, D G denotes the degree diagonal matrix of the graph G. Now, by the definition of the Laplacian, However, the degree of any vertex uv in the Cartesian product is deg(u) + deg(v), because all edges incident to a vertex will either be derived from one of the original graphs or the other, leading to corresponding nodes in the product graph.
Sentence 2: this work was supported by NSF grant #IIS-0705681 under the Robust Intelligence program.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This approach tackles a variant of (1) where the regularization term is replaced by an upper bound on the total variation norm; the associated constraint set is the convex hull of all Diracs and negatives of Diracs at elements of θ ∈ Θ, and thus adapted to conditional gradient algorithms [19].
Sentence 2: there is a direct link between the velocity field (5) and the functional F . The differential of F evaluated at µ ∈ M(Ω) is represented by the function F (µ) : Ω → R defined as Thus v t is simply a field of (minus) subgradients of F (µ m,t )-it is in fact the field of minimal norm subgradients.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We can simplify this MLN by replacing R by a predicate J having one argument such that D(1 Decomposition.
Sentence 2: given an MLN M and its associated schematic MLN S, the optimum solution to the Integer Polynomial Programming problem returned by SMLN-2-IPP(S) is the MAP solution of M . In the next three examples, we show the IPP output by Algorithm 2 on some example MLNs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We examine the efficiency of our MCMC method with approximate metric on a well studied toy example, the Fitzhugh-Nagumo model, before examining a realistic, nonlinear and highly challenging example describing enzymatic circadian control in the plant Arabidopsis thaliana [22].
Sentence 2: it has been shown that such chains may still be usefully employed as long as they satisfy some technical conditions, namely diminishing adaptation and bounded convergence [2].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, the differences in bounds reflect the intrinsic differences between risk minimizers.
Sentence 2: [7] has shown that we can estimate R(g) without any bias if satisfies the following symmetric condition: Specifically, let R u,− (g) = E X [ (g(X), −1)] = πE + [ (g(X), −1)] + (1 − π)R − (g) be a risk that U data are regarded as N data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Under this assumption, learning f i,j (t) is equivalent to learning a real number, α i,j .
Sentence 2: here, we adopt a method similar to [15] and approximate (4) by discretizing the integral: Intuitively, if δ is small enough and the triggering functions are bounded, it is reasonable to expect that i,t (λ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hierarchical multidimensional recurrent neural networks containing Long Short-Term Memory [11] hidden layers and a CTC output layer [8] have proven effective for offline handwriting recognition [9].
Sentence 2: if the prior P (α) is uniform and a single weight sample is taken for each element of D, then minimising L(α, β, D) is identical to minimising L N (w, D) with weight noise or synaptic noise [13].
Relationship: neutral
Domain: NeurIPS
Sentence 1: We learn a matrix of weights W ∈ d * p . In this model, each output is treated independently, so we can solve all of them quickly in one matrix operation (even with thousands of semantic features): where I is the identity matrix and λ is a regularization parameter chosen automatically using the cross-validation scoring function (Hastie et al., 2001) 3 .
Sentence 2: l( f) will take the prediction of features and return the closest point in a given knowledge base according the Euclidean distance (L 2 ) metric.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our proposed method significantly outperforms the correlation-based classifier which is unable to consistently track the attentional modulation of the listener over time.
Sentence 2: the complete data log-posterior, where the unobservable sequence {n k,r } K,R k=1,r=1 is given, takes the form: The log-posterior of the parameters given the complete data has a tractable functional form for optimization purposes.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, for any δ > 0, with probability at least 1 − δ, the following holds for h ∈ H: Furthermore, if H has a VC dimension of d, then the following holds with probability at least 1 − δ: where e is the natural number.
Sentence 2: the xaxis of the figures are in logarithmic scale.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now we provide a matching algorithmic lower bound on the expected regret, showing that the analysis presented in Section 3.1 is sharp as a function of T . Moreover, our lower bound characterizes how much regret must be accrued in order to achieve a specified estimation rate for the system parameters (A , B ).
Sentence 2: after each epoch, OFU requires optimizing a non-convex objective to O(T −1/2 ) precision.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Alternatively, the MAP problem can be solved in a lifted manner by leveraging various lifted inference rules such as the decomposer, the binomial rule [6,9,22] and the recently proposed single occurrence rule [13,19].
Sentence 2: our results show that for even small values of k (k bounds the partition size), our algorithm yields close to optimal MAP solutions, clearly demonstrating the power of our approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper, we deviate from this classic pipeline and propose to modulate the entire visual processing by a linguistic input.
Sentence 2: given a mini-batch B = {F i,•,•,• } N i=1 of N examples, BN normalizes the feature maps at training time as follows: where is a constant damping factor for numerical stability, and γ c and β c are trainable scalars introduced to keep the representational power of the original network.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With the same assumptions, [2] proves that for a single-hidden ReLU network with a single non-overlapping convolutional filter, all local minimizers of the population loss are global; they also give counter-examples in the overlapping case and prove the problem is NP-hard when inputs are not Gaussian.
Sentence 2: in these problems the inputs are labeled examples {(x i , y i )} n i=1 ∈ R d × R which are guaranteed to satisfy y i = f (⟨w, x i ⟩) for some w ∈ R d and nondecreasing (Lipchitz continuous) f ∶ R → R. The goal in this problem is to find a (nearly) accurate such f and w. An interesting polynomial-time algorithm called the Isotron exists for this problem [12,11].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Conditioned on σ = σ (j) , we define an HMM over G with the following transition and observation probabilities, respectively: L(z where φ(v, e; z1, .
Sentence 2: as we discuss in Section 5, the parametric assumptions made in the most basic form of ALPACA can be considerably relaxed without impacting the computational complexity of learning.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let k denote iteration count, T k denote time when iteration k starts for k 2 N. Initially, k = 0, T 0 = 0, and for t 2 [T k , T k+1 ), the policy is in iteration k. The iteration is updated from k to k + 1 when starting with t = T k , all ball-action (B i , a) pairs have been visited at least once.
Sentence 2: here the expectation is defined with respect to randomness introduced by Markov kernel of MDP as well as the policy ⇡.
Relationship: neutral
Domain: NeurIPS
Sentence 1: By the induction hypothesis, rounds 2 to n of the loop determine a cue permutation π ′ with INCORRECT(π ′ , L ′ ) ≤ (n − 1) • opt I ′ (L ′ ).
Sentence 2: in addition, we show that TTB does not have this property, concluding that the greedy method of constructing cue permutations performs provably better than TTB.
Relationship: neutral
Domain: NeurIPS
Sentence 1: On the word similarity task, SPPMI yields better results than SGNS, and SVD improves even more.
Sentence 2: we note that M PMI 0 is inconsistent, in the sense that observed but "bad" (uncorrelated) word-context pairs have a negative matrix entry, while unobserved (hence worse) ones have 0 in their corresponding cell.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Nevertheless, several questions remain open: whether there is an intrinsic information-theoretic obstacle to bridging this gap; whether our convergence rate estimates hold with high probability (and not just in expectation); and whether our analysis extends to a fully decentralized setting where the players' updates need not be synchronous.
Sentence 2: as we discussed above, the aggregate bias in the algorithm after n stages is O( ): if the conditions (5.2) are satisfied, both error terms vanish, but they might do so at very different rates.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is known that when n = ⌦(s ⇤2 log d), one could obtain the optimal statistical rate of O( p s ⇤ log d/n) by nonconvex method [37].
Sentence 2: in the low-dimensional setting, for two-layer neural network [14] propose a tensor-based method for estimating the parametric component.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Thus, if we can obtain lower bounds on accuracy for functionalities involving only a single bit at each of the parties, we obtain lower bounds on accuracy for all non-trivial general functionalities.
Sentence 2: a similar technique of transforming a non-linear optimization problem into an infinite dimensional LP has been successfully applied in [26], where optimal privatization mechanisms under local differential privacy has been studied.
Relationship: neutral
Domain: NeurIPS
Sentence 1: ( 6):  See Figure 1 for the plots of ρ * .
Sentence 2: the theory [11] behind LSH still works if we use hash function h 1 for preprocessing x ∈ S and a different hash function h 2 for querying, as long as the probability of the event {h 2 (q) = h 1 (x)} increases with Sim(q, x), and there exist p 1 and p 2 with the required property.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let us assume that each image of the database has been represented by a number of low-level features, and that a (dis)similarity measure has been defined so that the proximity between pairs of images represents some kind of "conceptual" similarity.
Sentence 2: it is interesting to note that while relevance feedback mechanisms have been first introduced in the information retrieval field [2], they are receiving more attention in the CBIR field (Huang).
Relationship: neutral