sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Recent work in generative adversarial networks (GANs) [33], variational autoencoders (VAEs) [34], and other generative models have achieved promising results on various semi-supervised classification tasks [35,36].
Sentence 2: we find that these models are not as well-suited for generic regression tasks such as in the UCI repository as for audio-visual tasks.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This means that any adjective placed on " will tend to be reconstructed correctly, and that its reconstruction is independent of the noun we have in position ¥ .
Sentence 2: the contributions from nouns and verbs in positions and £ are non-negligible, and notice how those given by words belonging to the subsets are almost symmetric to those given by words in the " subsets.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: This is harmless in some games, such as Pong where no reward is ever higher than 1 or lower than 1, but it is not satisfactory as this heuristic introduces specific domain knowledge that optimizing reward frequencies is approximately is useful as optimizing the total score.
Sentence 2: the clipping makes the DQN algorithm blind to differences between certain actions, such as the difference in reward between eating a ghost (reward >= 100) and eating a pellet (reward = 25) in Ms. Pac-Man.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: During training, the classifiers f i in the chain are trained to reduce the errors E(y i , ŷi ) by enriching the input vectors x with the corresponding previous true targets y <i as additional features.
Sentence 2: at test time, f i generates samples ŷi or estimates P (ŷ i |x, ŷ<i ) where ŷ<i are obtained from the preceding classifiers Another key limitation of PCCs is that the classifiers f i are trained independently according to a fixed label order, so that each classifier is only able to make predictions with respect to a single label in a chain of labels.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Another approximate k-NN idea is in [1], one of the first k-NN approaches to use a priority queue of nodes, in this case achieving a 3-fold speedup with an approximation to the true k-NN.
Sentence 2: these approaches are based on the notion that any points falling within a factor of (1 + ε) times the true nearest neighbor distance are acceptable substitutes for the true nearest neighbor.
Relationship: contrasting
Domain: NeurIPS
Sentence 1: Each pair (v i , g i ) ∈ V then generates a number of examples in this extended binary problem equal to the number of arcs of the p-graph g i for a total of N i=1 |A(g i )| examples.
Sentence 2: the set Z = {z a i } is linearly separable in the higher dimensional problem if and only if there exists a consistent solution for the original PLM problem.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The parameters are chosen by grid search over a small portion of data, and the parameters of the benchmark algorithms are fine-tuned (see Appendix F for details).
Sentence 2: we set the discretization level δ = 0.05, the window size z = 3, the step size η k = (kδ/20 + 100) −1 , and the regularization coefficient ζ i,j ≡ ζ = 10 −8 .
Relationship: entailment
Domain: NeurIPS
Sentence 1: We have conducted comprehensive performance evaluations by testing our method under different circumstances.
Sentence 2: to better understand the effect of augmenting logistic regression with semantic relatedness and use of overlapping-group-lasso penalty to enforce group level feature selection, we study the model adding only augmented logistic regression loss and adding only overlapping-group-lasso penalty separately, and compare with the APPLET method.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Average performance for different training/testing split proportions is in Figure 2  We next compare the performance on further benchmark datasets 1 by selecting training data via various biased sampling schemes.
Sentence 2: for the sampling distribution bias on labels, we use P (s = 1|y) = exp(a + by)/(1 + exp(a + by)) (datasets 1 to 5), or the simple step distribution P (s = 1|y = 1) = a, P (s = 1|y = −1) = b (datasets 6 and 7).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Estimating on-line the membrane potential of the presynaptic cell from its spiking history amounts to computing the posterior probability distribution, p (u t |s 1..t ).
Sentence 2: since equations 1 and 3 define a hidden Markov model, the posterior can be written in a recursive form: the posterior at time step t, p(u t |s 1..t ), can be computed by combining information from the current time step with the posterior obtained at the previous time step, p(u t−1 |s 1..t−1 ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: We will refer to the function 1 − RI( Ŝ, S) as the Rand index, although strictly speaking the Rand index is RI( Ŝ, S), the fraction of image pixel pairs on which the two segmentations agree.
Sentence 2: the Rand index is a measure of similarity, but we will often apply that term to a measure of dissimilarity.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In the medical diagnosis application, we can define F t (S) to be proportional to the number of candidate diseases which are eliminated after performing the set of tests S on patient t. If we assume that a particular test result always eliminates a fixed set of candidate diseases, then this function is submodular.
Sentence 2: this objective is the reduction in the size of the version space [5,6].
Relationship: entailment
Domain: NeurIPS
Sentence 1: The grid size was selected for economy of computation.
Sentence 2: the grid lower and upper bounds for were ad-hoc, though they were inspired by the literature, while for the same for C, we enlarged the lower range to focus on the region of the parameter space where the stability-based bounds have a better chance to be effective: the stability-based bounds grow with C in a linear fashion, with a coefficient that was empirically observed to be close to one.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We propose an upper bound for the expected total reward U * (T, B) of the oracle by relaxing the hard constraint to an average constraint and solving the corresponding constrained LP problem.
Sentence 2: let p j ∈ [0, 1] be the probability that the agent takes action k * j for context j, and 1 − p j be the probability that the agent skips context j (i.e., taking action A t = 0).
Relationship: entailment
Domain: NeurIPS
Sentence 1: That is, P (y = 1|x i = r) > P (y = 1|x i = r ) if r > r . • The monotonicity is non-trivial in that P (x i ) has positive probability for more than one feature value.
Sentence 2: there exists r > r and > 0 such that P (x i = r), P (x i = r ) > .
Relationship: entailment
Domain: NeurIPS
Sentence 1: More recently,  showed that by averaging the smoothed gradient estimates and still using the self-concordant barrier as regularization, one can achieve a regret of e O T 5/8 .
Sentence 2: denote by ḡt = 1 k+1 P k i=0 b g t i the average of the past k + 1 incurred gradients, where b g t i = 0 for t i  0.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Then we have inf Now, we claim that the mapping u � → regret � p (pred * � (u)) is continuous at u = u p . To see this, suppose the sequence {u m } converges to u p . Then we have The last equality holds by definition of pred * � .
Sentence 2: it is easy to see the term on the right goes to zero as u m converges to u p . Thus regret � p (pred * � (u m )) converges to regret � p (pred * � (u p )) = 0, yielding continuity at u p . this implies ∃δ > 0 such that where the last inequality holds since p � ψ * � (u) is a strictly convex function of u and u p is its unique minimizer.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The posterior mean µ t (x, ✓) and variance 2 t (x, ✓) conditioned on the previous observations (x 1 , ✓ 1 , y 1 ), ..., (x t 1 , ✓ t 1 , y t 1 ) are computed analogously to (5) [20].
Sentence 2: a robust optimization formulation in this setting is to seek x that solves we seek to find a configuration x that is robust against any possible parameter vector ✓ 2 ⇥.
Relationship: entailment
Domain: NeurIPS
Sentence 1: As computational objects, they explicitly distinguish between the sampler for the random variables from their joint distribution, and the assessor of their joint density.
Sentence 2: a CGPM is required to sample/assess the joint distribution of a subset of output variables x [r,Q] conditioned on another subset x [r,E] , and marginalizing over Listing 1 Computational interface for composable generative population models.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For the closed convex cone W(x) := conv cl cone(R − x), and for any x, x ′ ∈ R, In other words, Next, we formulate the test as a convex optimization program, when a finite number of samples are given.
Sentence 2: using the samples in X ⊂ R instead of all the points in R, we can define an approximation of W(x) as which is the tangent cone (also known as the descent cone) at x with respect to the data hull conv(X).
Relationship: entailment
Domain: NeurIPS
Sentence 1: First, we observe that the random initialization C 1 , C 2 is necessarily somewhat biased, in the sense that C 1 and C 2 never divide P 1 exactly into two halves.
Sentence 2: ||C 1 ∩ P 1 | − |C 2 ∩ P 1 || ≥ N − 1 2 − with high probability.
Relationship: entailment
Domain: NeurIPS
Sentence 1: clusters where each training example and its k-nearest points have same label and where points differently labeled are distanced by an additional safety margin.
Sentence 2: given n input examples x 1 , ..., x n in ℜ D and corresponding class labels y 1 , ..., y n , the technique in [9] learns the D × D transformation matrix L that optimizes the following objective function: where η ij ∈ {0, 1} is a binary variable indicating whether example x j is one the k-closest points of x i that share the same label y i , c is a positive constant, y il ∈ {0, 1} is 1 iff (y i = y l ), and h(s) = max(s, 0) is the hinge function.
Relationship: entailment
Domain: NeurIPS
Sentence 1: [2005] observed that for suitable cost-weighted losses, one may use (4) to solve density sublevel set estimation.
Sentence 2: let : {±1} × R → R be any classification-calibrated loss (e.g., hinge or logistic) in the sense of [Zhang, 2004, Bartlett et al., 2006.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The Thurstonian view described in the finite model can be easily extended to the nonparametric one, where a partial ranking (X ρ 1 . . . X ρ m ) can be generated as the first m items to arrive in a race.
Sentence 2: for each atom X k let z k ∼ Exp(w k ) be the time of arrival of X k and X ρ i the ith item to arrive.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Either of the following assumptions would suffice: (A2) p is continuous not only on X • but also on ∂X (i.e., p(x) → 0 as dist(x, ∂X ) → 0).
Sentence 2: (A3) p is supported on all of R D . the support of p has no boundary.
Relationship: entailment
Domain: NeurIPS
Sentence 1: 2  Given the above system model, we formulate the distributed matrix multiplication problem based on the following terminology: We define the computation strategy as the 2N functions, denoted by that are used to compute each Ãi and Bi .
Sentence 2: for any integer k, we say a computation strategy is k-recoverable if the master can recover C given the computing results from any k workers.
Relationship: entailment
Domain: NeurIPS
Sentence 1: . . , x T , the goal is to find a low-dimensional approximation of this data that minimizes the 2-norm approximation error.
Sentence 2: we want to find a rank k projection matrix P and a bias vector b ∈ R n such that the following cost function is minimized: Differentiating and solving for b gives us b = (I − P ) x, where x is the data mean.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Although a developmental approach to the velocity estimation task is shown to be beneficial, it is not the case that all developmental progressions that lead to performance advantages on the disparity estimation task also lead to advantages on the velocity estimation task.
Sentence 2: a coarse-to-multiscale developmental system outperformed non-developmental and random developmental systems on the velocity estimation task, but a fine-to-multiscale system did not.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In large-scale problems, the linear-equation solution sequence {∆" k } is generated iteratively while seeking a trial step ∆" in the inner iteration process, and the parameter sequence {"i}, whose two consecutive elements are denoted by "now and " next , is produced by the outer iteration (i.e., epoch in batch mode).
Sentence 2: the outer iterative process updates parameters by " next = "now + ∆" without taking any uphill movement: if the step is not satisfactory, then R is decreased so as to realize an important Levenberg-Marquardt concept: the failed step is shortened and deflected towards the Cauchy-step direction simultaneously.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The scheduling problem is to decide which nodes should transmit at a given time over a given frequency, so that (a) there is no interference, and (b) nodes which have a large amount of data to send are given priority.
Sentence 2: it is well known that if each node is given a weight equal to the data it has to transmit, optimal network operation demands scheduling the set of nodes with highest total weight.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Under the curvature condition in (8) on the boundaries between k and classes in A c , our result shows that the robustness to random and semi-random noise exhibits the same behavior that has been observed earlier for linear classifiers in Theorem 1.
Sentence 2: r * S 2 is precisely related to the adversarial robustness r * 2 by a factor of d /m.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Specifically, the un-normalized Fredholm kernel from Eqn 6 can be rewritten as: Thus k F (x, z) is simply an inner product which depends on both the unlabeled data distribution p(x) and the "inner" kernel k H . This inner product re-weights the standard norm in feature space based on variances along the principal directions of the matrix Σ F . We show that for the model when unlabeled data is sampled from a normal distribution this kernel can be viewed as a "soft thresholding" PCA, suppressing the directions with low variance.
Sentence 2: we have the following 3 and assume the distribution p X for unlabeled data is a single multi-variate normal distribution, N (µ, diag(σ 2 1 , .
Relationship: entailment
Domain: NeurIPS
Sentence 1: We prove that ProxSVRG+ improves/generalizes several well-known convergence results (e.g., ProxGD, ProxSGD, ProxSVRG/SAGA and SCSG) by choosing proper minibatch sizes.
Sentence 2: proxSVRG+ is ) times faster than ProxGD, which partially answers the open problem (i.e., developing stochastic methods with provably better performance than ProxGD with constant minibatch size b) proposed in [24].
Relationship: entailment
Domain: NeurIPS
Sentence 1: We consider relational data consisting of triplets that encode the existence of relation between two entities that we will call the subject and the object.
Sentence 2: we consider a set of n s subjects {S i } i∈ 1;ns along with n o objects {O k } k∈ 1;no which are related by some of n r relations {R j } j∈ 1;nr .
Relationship: entailment
Domain: NeurIPS
Sentence 1: Following the argument used in [17] for a smoothed original estimate of the ROC curve, one may show that a smoothed bootstrap of the studentized statistic r n (α)/σ n (α) yields a better pointwise rate of convergence than 1/ √ n, the one of the gaussian approximation in the Central Limit Theorem.
Sentence 2: for a given α ∈]0, 1[, if the bandwidth used in the computation
Relationship: entailment
Domain: NeurIPS
Sentence 1: These conditional probabilities Y ad ¢b vS g T # define our new representation for the examples.
Sentence 2: each point T is associated with a vector of conditional probabilities Y ¤d ¦b vS g T # , S ( F e¥ ¨ § © § ¨ § ¨¥ 8y .
Relationship: entailment
Domain: NeurIPS
Sentence 1: [31] to provide a general Optimistic Values Theorem in Appendix B.
Sentence 2: similar to online learning, we can guarantee that greedy-action selection according to upper-confidence values will converge to the optimal policy, if the confidence interval radius shrinks to zero, if the algorithm to estimate action-values for a policy converges to the corresponding actions and if upper-confidence estimates are stochastically optimal-remain above the optimal action-values in expectation.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Since Theorem 1 proves that the localization error per data point is bounded by a constant given an OCC, in practice we only need to minimize the data reconstruction error in order to minimize the upper bound of the localization measure.
Sentence 2: we need to solve the following problem: This optimization problem is quite similar to sparse coding [12], except that there exists the orthogonal constraint on the basis vectors.
Relationship: entailment
Domain: NeurIPS
Sentence 1: However, as the postsynaptic neuron does not have direct access to the presynaptic membrane potentials, only to the spikes emitted by its presynaptic partners based on those potentials, computing the required function becomes a non-trivial inference problem.
Sentence 2: neurons need to perform computations on their inputs in the face of significant uncertainty as to what those inputs exactly are, and so as to what their required output might be.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In this paper, we discuss an alternative: a discriminative framework in which we assume that supervised side information is present, and in which we wish to take that side information into account in finding a reduced dimensionality representation.
Sentence 2: we present DiscLDA, a discriminative variation on Latent Dirichlet Allocation (LDA) in which a class-dependent linear transformation is introduced on the topic mixture proportions.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Next, we define this distribution which is essentially a truncated Geometric distribution.
Sentence 2: given parameters ε ∈ (0, 1) and the polynomial growth rate ρ (with constant C) of the graph, define ϕ = ε 5C2 ρ , and Then, the distribution (or random variable) Q is defined over integers from 1 to K(ε, ρ) as (1) Initially, select x ∈ Σ n arbitrarily.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We propose a novel deep kernel learning model and stochastic variational inference procedure which generalizes deep kernel learning approaches to enable classification, multi-task learning, additive covariance structures, and stochastic gradient training.
Sentence 2: we apply additive base kernels to subsets of output features from deep neural architectures, and jointly learn the parameters of the base kernels and deep network through a Gaussian process marginal likelihood objective.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The basic statistical properties of natural sounds, as observed through a linear filter, have been previously documented by Attias [13].
Sentence 2: he showed that, as with visual images, the spectral energy falls roughly according to a power law, and that the histograms of filter responses are more kurtotic than a Gaussian (i.e., they have a sharp peak at zero, and very long tails).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Given two equivalence relations ∼ 1 and ∼ 2 , the refinement ∆(∼ 1 ) ∆(∼ 2 ) holds if and only if s ∼ 2 s ⇒ s ∼ 1 s and s ∼ 2 s ⇒ ∀a ∈ A, ∀C ∈ S/∼ 1 P a (s)(C) = P a (s )(C) .
Sentence 2: ∀s, s with s ∼ Γn+1 s , and ∀C ∈ S/∼ Γn , P a (s)(C) = P a (s )(C).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Slow Feature Analysis [1] combines many of the best properties of these methods to provide a good general nonlinear model.
Sentence 2: it uses an objective function that minimises the first-order temporal derivative of the outputs; it provides a closedform solution which maximises this function by projecting inputs into a nonlinear http://www.loria.fr/equipes/cortex/ space; it exploits sphering (or PCA-whitening) of the data to ensure that all outputs have unit variance and are uncorrelated.
Relationship: entailment
Domain: NeurIPS
Sentence 1: If G = (V, E) is the network that we want to fit our model to, and uv denote the graph that we obtain by resampling the value of X uv in G uv according to the conditional distribution P (X uv | x Guv \ {x uv }; θ) predicted by our model.
Sentence 2: g * uv is the result of performing just one iteration of Gibbs sampling on X uv using θ, where the configuration x Guv of G uv is used to initialize the (single-step) Markov chain.
Relationship: entailment
Domain: NeurIPS
Sentence 1: This reference set of boxes may be a uniform sub-sampling of the space of windows as done in Sliding Window methods, or may itself be the output of another object proposal method such as Selective Search [39].
Sentence 2: each greedy augmentation step under our formulation given by: argmax (7b) Intuitively speaking, the marginal gain of a new window y under our diversity function is the largest gain in coverage of exactly one of the references boxes.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Discrete-time finite-horizon LQR is a well-studied control method that optimizes a convex quadratic objective function with respect to affine state-transition dynamics from an initial system state x init .
Sentence 2: lQR finds the optimal nominal trajectory τ ⋆ 1:T = {x t , u t } 1:T by solving the optimization problem From a policy learning perspective, this can be interpreted as a module with unknown parameters θ = {C, c, F, f }, which can be integrated into a larger end-to-end learning system.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Let the preference constraint (v i , g i ) ∈ V be selected at a given iteration, to enforce the constraint a∈A(gi) α a i + λ i = C, λ i ≥ 0, two elements from the set of variables {α a i |a ∈ A(g i )} ∪ {λ i } will be optimized in pairs while keeping the solution inside the feasible region α a i ≥ 0.
Sentence 2: let χ 1 and χ 2 be the two selected variables, we restrict the updates to the form χ 1 ← χ 1 −ν and χ 2 ← χ 2 +ν with optimal choices for ν.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The algorithmic strategy will look for a sequence {J n , ι n } ∞ n=1 , where J n ⊂ Q is a set of covering prototypes, and ι n : J n → F S is a function that associates a feature to every prototype in J n . Starting with J 0 = ∅ and Γ 0 = ∅, the strategy needs to find, at step n > 0, a cover Ĵn for S, based on the distance metric D(Γ n−1 ).
Sentence 2: it has to guarantee that ∀s ∈ S, ∃κ ∈ Ĵn with D(Γ n−1 )(s, κ) = 0.
Relationship: entailment
Domain: NeurIPS
Sentence 1: If f (n) grows asymptotically faster than √ n, then one can "sparsify" f (n) so that it will be crossed with an arbitrarily small probability.
Sentence 2: a boundary with the form in Equation ( 8) can be constructed to bound the threshold-crossing probability below any δ (part 2 of the Theorem).
Relationship: entailment
Domain: NeurIPS
Sentence 1: We have traced an analytical connection from psychophysical results in monkey and man to a broad class of machine-learning algorithms, namely, density estimation in latent-variable models.
Sentence 2: behavioral studies of multisensory integration have shown that primates estimate stimulus properties with the peak of the posterior distribution over the stimulus, conditioned on the two unisensory cues [3,4].
Relationship: entailment
Domain: NeurIPS
Sentence 1: In particular, it is of great interest to find (N, δ) as a monotonically decreasing function in both N and δ ∈ (0, 1) such that the solution x N +1 satisfies Pr (φ(x N +1 ) − φ(x * ) ≥ (N, δ)) ≤ δ.
Sentence 2: we want to show that with probability at least 1 − δ, φ(x N +1 ) − φ(x * ) < (N, δ).
Relationship: entailment