sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: This is because the choice of q(x) for G-BP is favored by log-supermodular models, i.e., most of configurations are concentrated around (0, 0, • • • ) similar to the choice (7) of q(x) for G-BP.
Sentence 2: this implies that G-BP generalizes BP well: the former provides a lower bound of Z for any GMs, while the latter does only for log-supermodular GMs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Suppose that H is any triangulated subgraph of G. Let P G (i) and P G (j) be the (marginalized) distributions of P G on V (i) and V (j) respectively, and P H (i) and P H (j) be the (marginalized) distributions of the distribution P H on V (i) and V (j) where ) ] and The following result assures us that the KL-divergence also factors according to the separator  Proof.
Sentence 2: a graphical model is a pair (G, P ) where P is the joint probability distribution for random variables X 1 , X 2 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We start from the conductance-based neuron model [1]: where, ḡleak =: g leak /C m , J ion =: I ion /C m , J syn (t) := I syn (t)/C m , V is the membrane voltage, ḡleak is the normalized leak conductance, E leak is the reversal potential, J ion are the voltage-dependent ionic inputs, ⃗ w := (w 1 , w 2 , • • • , w d ) are the gating variables that characterize the states of ion channels, J syn is a synaptic input, C m is the membrane capacitance, I ion are the voltage-dependent ionic currents and I syn (t) is a synaptic input current.
Sentence 2: in our examination of biological data, we have explored parameters empirically from current-voltage data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Using all KM nodes to obtain stochastic gradient estimates at the same point, we can perform T iterations of A-MB-SGD with a mini-batch size of KM , yielding an upper bound of This is a reasonable and common approach, and it is optimal (up to constant factors) when KM = O( L 2 H 2 T 3 ) so that the statistical term is limiting.
Sentence 2: . . z n } in parallel (⇤), and sequential variance-reduced stochastic gradient updates in between (⇤⇤).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let T denote the estimated transition model based on data ∆, which approximates the true model T . In general, we assume that learning T (s, a) implies minimizing the loss L( T (s, a); D s,a ) where D s,a = {s i } ns,a i=1 are the successor states in the transitions (s, a, s i ) from s, a in ∆.
Sentence 2: if ζ(s, a) is small, then the last k visitations in the data-set D s,a did not have a significant effect on improving T and in turn s, a does not require further exploration.
Relationship: neutral
Domain: NeurIPS
Sentence 1: T log log T for some universal constant C 1 ą 0; furthermore, there exists another universal constant C 2 ą 0 such that no policy can achieve worst-case regret smaller than C 2 ?
Sentence 2: one exception is our LIL-TRISECT algorithm, in which we remove the coefficient of 4 in front of the square root term in the confidence bands in Eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Putting Together: We are now ready to pose our general optimization problem: The objective function penalizes excess loss and ensures through the second term that this excess loss can be enforced through admissible gating functions.
Sentence 2: another set of related work includes classifier cascade [5] and decision DAG [3], both of which aim to re-weight/re-order a set of pre-trained base learners to reduce prediction budget.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A crucial exception to this perspective occurs when γ (t+1) is highly sparse, or nearly so, in which case there are limited degrees of freedom with which to model even small differences between some φ i and φ i .
Sentence 2: here we first empirically examine the trajectories of SBL iterations produced via the LSTM-like rules derived in Section 2.3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Assuming that the hypothetical units can be replaced by time-bounded general recurrent networks, we determine an upper bound on the VC dimension of the resulting networks in terms of size and computing time using an idea from Koiran and Sontag (1998) and Proposition 1.
Sentence 2: we emphasize that the only constraint on the parameters of the product units is that they yield real-valued, that is, not complex-valued, functions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, the vanishing gradient effect is a well-known hardship to backpropagate an error signal through a long-range temporal interval.
Sentence 2: since the sentence sequence generation from image streams has not been addressed yet in previous research, we instead extend several state-of-the-art single-sentence models that have publicly available codes as baselines, including the log-bilinear multimodal models by Kiros et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We first show a strong hardness result: there is no 1/n γ c approximation for influence maximization (unless P = NP) for all networks with up to n γ ε-almost submodular nodes, where γ is in (0, 1) and c is a parameter depending on ε.
Sentence 2: the process ends when no new node becomes active in a step.
Relationship: neutral
Domain: NeurIPS
Sentence 1: LSTD-Q learns a control policy π from a batch of samples by estimating a linear approximation Qπ = Φw π of the action value function Q π ∈ R |S||A| , where w π ∈ R k are a set of weights and Φ ∈ R |S||A|×k is a feature matrix.
Sentence 2: moreover, the BP regularizer was not sensitive to the scale of the regularization coefficient.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A key aspect of PDCTs is their spatial adaptivity, which enables local (rather than global) polynomial fitting of the decision boundary.
Sentence 2: we also study DCTs equipped with polynomial classification rules at each leaf, and show that as the smoothness of the boundary increases their errors converge to the Bayes error at a rate approaching n −1/2 , the parametric rate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Principal component analysis (PCA) has been applied profitably to neuronal recordings (see for example [14]) but these analyses often plot activity trajectories corresponding to different network states using the fixed principal component coordinates derived from combined activities under all stimulus conditions.
Sentence 2: although chaotic intrinsic activity can be completely suppressed by the input in this network state, its imprint can still be detected in the spatial pattern of the non-chaotic activity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our method (as well as the static low rank method based on the low rank hypothesis) however fails when the rank of S(t) is high.
Sentence 2: given the last adjacency matrix A T , a set of features Φ, and an estimate F of F T +1 based on the sequence of adjacency matrices A t , t ∈ {1, 2, ..., T }, we want to find a matrix S which fulfills the following requirements: • S has low rank -this is a standard assumption in matrix completion problems [15].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Appealingly, the advantage of NPNBP grows with the domain size due to the growth in complexity of matrix inversion.
Sentence 2: copulas are "distribution generating" functions that allow us to separate the choice of the univariate marginals and that of the dependence structure, encoded in the copula function C. Importantly, this flexibility often results in a construction that is beneficial in practice.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Beginning with a comparison to KTF, fix θ ∈ H k+1 d (L), corresponding to evaluations of f ∈ H(k + 1, L; [0, 1] d ), and consider a point x ∈ Z d that is away from the boundary.
Sentence 2: an extension of trend filtering to additive models was given in [21].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let θ (H−1) * be a critical point of L H−1 with γ * H−1 = 0, and θ λ be a parameter given by eq.
Sentence 2: in mixture of FA and PCA, this does not necessarily work well, because the decomposition V = F F T + S does not give a natural parametrization.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the architecture of Figure 1, we can use independent samples of x ∼ D 1 at the input and instead of imposing a Gaussian distribution on the latent code, we can impose the distribution of the second domain using its independent samples y ∼ D 2 .
Sentence 2: the question that has remained unanswered is whether it is possible to achieve a complete decomposition of content and style in an unsupervised fashion, where the class label or discrete structure information is encoded in the latent code z, and the remaining continuous structure such as style is captured by a powerful and deep PixelCNN decoder.
Relationship: neutral
Domain: NeurIPS
Sentence 1: samples {(x i , y i )} m i=1 ∈ B d × [0, 1], from an unknown distribution D. We assume that there exists a predictor w * ∈ R d such that E (x,y)∼D [y|x] = φ w * , x , where φ is an activation function.
Sentence 2: • We introduce a new setup: stochastic optimization of locally-quasi-convex functions; and show that this setup captures Generalized Linear Models (GLM) regression, [14].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, as we are considering G to be a grid, both estimators in (4), ( 5) can be computed very quickly, in nearly O(n) time, since the columns of V here are discrete cosine transform (DCT) basis vectors when d = 1, or Kronecker products thereof, when d ≥ 2 (e.g., [9,17,20,28]).
Sentence 2: even the best linear smoothers have the same poor performance as the mean over T d (C n ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Further, if the observed affinity scores from various explicit and implicit feedback are treated as exact (or mildly perturbed) entries of the unobserved preference value matrix, then the preference completion task naturally fits in the framework of low rank matrix completion [22; 38].
Sentence 2: the bound provides a trade-off between observable training error and complexity defined by nuclear norm of the estimate.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The Euclidean metric in R N induces a metric g E (θ) = v(θ) • v(θ) on the curve, so that the distance dL E moved in R N as one moves from θ to θ + dθ on the curve is dL E = g E (θ)dθ.
Sentence 2: now at each point θ, when both are nonzero, v(θ) and a(θ) span a 2 dimensional subspace of R N . Within this subspace, there is a unique circle of radius R(θ) that has the same position, velocity and acceleration vector as the curve h(θ) at θ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Section B, we provide a common technique, regression calibration to deal with measurement error problem.
Sentence 2: we conduct a general risk analysis of this framework and in particular, we show for the first time, if two domains are related, HTL enjoys faster convergence rates of excess risks for Kernel Smoothing and Kernel Ridge Regression than those of the classical non-transfer learning settings.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our policy model consists of a recurrent neural network (RNN) decoder coupled with an attention mechanism.
Sentence 2: [35], which extracts the relevant information from the inputs using a variable-length alignment vector a t . a t specifies how much every input data point might be relevant in the next decoding step t. Let xi t = (s i , di t ) be the embedded input i, and h t ∈ R D be the memory state of the RNN cell at decoding step t. The alignment vector a t is then computed as ) Here ";" means the concatenation of two vectors.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Though units of α are consistent with a general optimization setting where step-size has units of objective −1 , in these problems, picking a good α that is consistent with the scales of the reward was difficult.
Sentence 2: this architecture can also be interpreted as a two layer neural network: the bottom layer is clamped with random weights, a sinusoidal activation function is used, and the top layer is finetuned.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each brain-image was processed using the Configurable Pipeline for Analysis of Connectomes (CPAC) [27].
Sentence 2: x lives on a swissroll embedded in a  Our goal is to develop an approach to learn about f Y |X from n pairs of observations that we assume are exchangeable samples from the joint distribution, , where [n] = {1, . . . , n}.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We evaluated the usefulness of our architectures for control in two ways: 1) by replacing emulator frames with predicted frames in a previously-learned model-free controller (DQN; DeepMind's state of the art Deep-Q-Network for Atari Games [21]), and 2) by using the predicted frames to drive a more informed than random exploration strategy to improve a model-free controller (also DQN).
Sentence 2: we approximate the tensor by factorizing into three matrices as follows [33]: where and f is the number of factors.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Other lines of research which are related to this paper are multiple-instance learning (MIL) problems [1,5,10], and multi-instance multi-label learning (MIML) problems [24,25] which extends the binary MIL setup to multi-labels scenario.
Sentence 2: in this paper, we investigate a special kind of semi-supervised learning which considers ambiguous labels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For instance, non-stationary dynamic Bayesian networks are introduced in [9], where the structures are learned via MCMC sampling; such approach is not likely to scale up to more than 1000 nodes and without a regularization term it is also prone to overfitting when the dimension of the data is high but the number of observations is small.
Sentence 2: we propose a kernel reweighted 1 -regularized auto-regressive approach for learning this sequence of networks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Complex numbers are represented in the polar form as z = |z|e iφz with |z| ∈ R + denoting the magnitude of z and φ z ∈ [0, 2π) denoting the phase.
Sentence 2: there are of course many other implicit and explicit sources of inductive bias-here we show that merely parameterizing transformations via convolutions and using gradient descent for training already induces sparsity in the frequency domain.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As in recent methods [12], we build on the observation that the Newton direction computation is a Lasso problem, and perform iterative coordinate descent to find its solution.
Sentence 2: moreover, for p = 10000 random pattern, there are p 2 = 100 million variables, the selection of fixed/free sets helps QUIC to focus only on very small part of variables, and can achieve an accurate solution in about 15 minutes, while other methods fails to even have an initial guess within 8 hours.
Relationship: neutral
Domain: NeurIPS
Sentence 1: where Li is the instantaneous linear response of filter i, 0' is a constant and Wji controls the strength of suppression of filter i by filter j.
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: neutral
Domain: NeurIPS
Sentence 1: The proposed model is a semiparametric methodology, which offers modeling flexibilities and reduces the effect of model misspecification.
Sentence 2: for instance, in 1950 and 2000, topic 9 (related to mouse, cells, human, transgenic) and topic 17 (related to virus, rna, tumor, infection) are highly correlated.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Hence, y w (x) is obtained by solving the so-called inference problem, which is known to be N P-hard for many output feature maps [6,7].
Sentence 2: we observe, from Figure 1, on some datasets (e.g., Medical, NCI60), that the inference task is very easy since exact inference can be computed for most of the examples even with K values that are below 50% of the number of microlabels.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Now, the remaining problem is how to efficiently draw samples from p(Θ, Z, Φ) and estimate the expectations E[z] as accurate as possible, which are needed in learning classification models.
Sentence 2: directly applying importance sampling to p(Θ, Z, Φ) may cause some issues since importance sampling suffers from severe limitations in large sample spaces.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We used a 2×2 within subject factorial design for this experiment, testing for the effect of the retrieval mode -recognition/recall and either a stimulus heavy, or cue heavy selection of task materials.
Sentence 2: mcClelland's equally influential CLS model is explicitly a dual-process model, where a fast learning hippocampal component primarily responsible for recollection sits atop a slow learning neocortical component responsible for familiarity [9].
Relationship: neutral
Domain: NeurIPS
Sentence 1: (2016) implies that, for the probabilistic s-step Adams-Bashforth integrator, the exponent ⇢ should be taken to be 2s + 1.
Sentence 2: it is still a three-part procedure, analogous for example to paired Adams-Bashforth and Adams-Moulton integrators used in PEC mode (Butcher, 2008).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Bayesian observer models are very effective in describing human performance in perceptual tasks, so much so that they are trusted to faithfully recover hidden mental representations of priors, likelihoods, or loss functions from the data.
Sentence 2: we determine the shape of p meas (x|s) with a maximum-entropy approach by fixing the first four moments of the distribution, and under the rather general assumptions that the sensory measurement is unimodal and centered on the stimulus in internal measurement space.
Relationship: neutral
Domain: NeurIPS
Sentence 1: LSPI solves an infinitehorizon variant of problem (9) with discount factor λ = 0.9, polynomial basis features of degree 3 and a discrete action space comprising 1,000 points sampled uniformly from the true continuous action space.
Sentence 2: we emphasize that all systematic estimation errors of this type accumulate as they are propagated through the dynamic programming recursions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Mean shift: All the three distributions are isotropic multivariate normal distributions: p = N ([0.5, 0, . . . , 0], I), q = N ([1, 0, . . . 0], I), and r = N (0, I), defined on R 50 .
Sentence 2: fID requires computing the square root of the feature covariance matrix (2048 x 2048), and is computationally too expensive for permutation testing.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the reward function is KWIK learnable through linear regression [7] and though DBN CPTs with small parent sizes are also KWIK learnable, the high connectivity of this particular DBN makes autonomous exploration of all the parent-value configurations prohibitive.
Sentence 2: we need to show: (i) The number of steps between traces where V A < V T − is polynomially bounded.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Aggressive SHAMO with prior achieves average error of 1.47 (vs. 2.73 with no prior) on 1-vs-1 USPS and 4.97 (vs 4.93) on one-vs-rest USPS, with score rank of 1.0 (vs 2.9) and 1.7 (vs 2.0) respectively.
Sentence 2: 1 by noting that, there is a multiclass mistake if there is at least one prediction mistake of one of the one-vs-rest problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If v is influenced at time t, add v to S t . The process stops at T if S T = ∅ at the end of the step t = T . The set of the influenced nodes at the end of propagation is defined as S = ∪ T −1 i=0 S t . We often refer an edge (u, v) being open if node u influences node v. The IC model is equivalent to the live-arc graph model, where the influence happens at once, rather than sequentially.
Sentence 2: the bounds can be efficiently obtained by message passing implementation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We study the runtime required to learn a predictor such that with high probability over the choice of S, the error rate of the learnt predictor satisfies L γ (w) .
Sentence 2: [2012] have shown that without utilizing kernels, no convex surrogate loss can guarantee an approximation factor smaller than α < 1 2 ( 1 γ − 1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The proof alongside the derivation of the ELBO for BLR can be found in the Appendix Theorem 2.
Sentence 2: we make BOCPD robust by using β-D posteriors p βrlm (r t , m t |y 1:t ), π βp m (θ m |y 1:t ) for β = (β rlm , β p ) > 0 1 . β rlm prevents abrupt changes in p βrlm (r t , m t |y 1:t ) caused by a small number of observations, see section 2.3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In our setting we can only ever determine that an arm is in H 1 and not H 0 , but it is impossible to detect that an arm is in H 0 and not in H 1 .
Sentence 2: because µ 0 is known, there exist schemes that guarantee FDR-or FWER-even if the arm means µ i and the cardinality of H 1 are unknown (see Section 2.1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is easy to understand why this occurs by considering the prior distribution over amplitude and phase implied by our choice of prior distribution over x t (or equivalently over z t ), Phase and amplitude are dependent in the implied distribution, which is conditionally a uniform distribution over phase when the amplitude is zero and a strongly peaked von Mises distribution [15] when the amplitude is large.
Sentence 2: we have demonstrated the utility of the new method on synthetic and natural signals, where it outperformed conventional approaches.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In general, it is not possible to give a more explicit version of the critical time of Corollary 3, or of the anytime influence bound of Proposition 2.
Sentence 2: while the first algorithms focused on discrete-time models and the special case T = +∞ [3,4], subsequent papers [5,6] brought empirical evidences of the key role played by temporal behavior.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , i |i| ) of indices i j ∈ {1, . . . , m} such that i 1 < i 2 < .
Sentence 2: it consists of choosing the (Boolean-valued) feature i with the largest utility U i defined as where N i is the set of negative examples covered (classified as 0) by feature i, P i is the set of positive examples misclassified by this feature, and p is a learning parameter that gives a penalty p for each misclassified positive example.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since our definition of each vocabulary shape model assumes that its parts are conditionally independent, we can calculate the likelihood of the part hypotheses ) by taking a product over the individual likelihoods of the parts: The term stands for the spatial constraint imposed by a vocabulary edge e Ri between a parent hypothesis z R and its part hypothesis 1) is above a threshold, we add edges between z R and its most likely part hypotheses.
Sentence 2: we employ a second step which revisits each class separately.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We will in the following consider tree-consistent partitions, where each data block in a partition corresponds to exactly one node for a cut (possibly across different levels) in the tree-see Figure 1.
Sentence 2: the last plot in Figure 4 reveals an important difference between chunky EM and CS-EM: with a fixed ratio between number of data points and number of clusters, the EM-speedup declines a lot for chunky EM, as the number of clusters and data points increases.
Relationship: neutral