sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Here, p is the total number of features (or covariates) and n is the total number of observations (or the sample size).
Sentence 2: this approach, which we call TREEWEIGHT, calculates the feature importance score for a variable by summing the impurity reductions over all nodes in the tree where a split was made on that variable, with impurity reductions weighted to account for the size of the node.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We consider this centralized ERM objective for m parties, each with a data set D j of size n j : i , y The parties can collaboratively learn a differentially private model via iterative learning by adding noise to the aggregated gradients within the MPC in each iteration with the following noise bound.
Sentence 2: using Lemma 2.1, (1) σ 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: When both G AB and G BA are learned simultaneously, there is an analog expression L GAN (G BA , D A , pB , pA ), in which the domains A and B switch roles and the two losses (and four networks) are optimized jointly.
Sentence 2: it requires that pairs of samples are transfered at once, which, while having little implications on the training process as it is currently done, might effect the ability to perform on-line learning.
Relationship: neutral
Domain: NeurIPS
Sentence 1: According to [1], the above condition is the weakest condition to guarantee that optimizing a surrogate loss function will lead to obtaining a model achieving the Bayes risk (in our case, the top-k Bayes ranker), when the training sample size approaches infinity.
Sentence 2: it is easy to verify that Proposition 8 holds for this case while the opposite does not.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Results in terms of minimum ESS are summarized in Table 2.
Sentence 2: in addition, we show that ⇢(y t , y t+h ) is a non-negative decreasing function of the time lag in discrete steps h. The variance of a Monte Carlo estimator is determined by its Effective Sample Size (ESS) [18], defined as ESS = N/(1 + 2 ⇥ P 1 h=1 ⇢ x (h)), where N is the total number of samples, ⇢ x (h) is the h-step autocorrelation function, which can be calculated in a recursive manner.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This increases the size of the subgame compared to the inexpensive method because a strategy must be recomputed for every action a ∈ A(h) in addition to a.
Sentence 2: formally, an imperfect-information subgame is a set of nodes S ⊆ H such that for all h ∈ S, if h h , then h ∈ S, and for all h ∈ S and all i ∈ P, if h ∈ I i (h) then h ∈ S. Define S top as the set of earliest-reachable nodes in S. h ∈ S top if h ∈ S and h ∈ S for any h h. This section reviews prior techniques for subgame solving in imperfect-information games, which we build upon.
Relationship: neutral
Domain: NeurIPS
Sentence 1: samples from D will produce an -optimal solution x to the problem (namely, F (x) ≤ min x∈K F (x) + ) with probability at least 1 − δ?
Sentence 2: let K be a unit 2 ball and F be the set of all convex sub-differentiable functions with Lipschitz constant relative to 2 bounded by 1 or, equivalently, ∇f (x) 2 ≤ 1 for all x ∈ K. Then, known algorithm for SCO imply that sample complexity of this problem is O(1/ 2 ) and often expressed as 1/ √ n rate of convergence (e.g.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To change the size of the intermediate representation, one can replace x with x obtained by suitably sub-sampling or zero-padding x.
Sentence 2: a plain feedforward neural network typically consists of L layers where the l th layer (l ∈ {1, 2, ..., L}) applies a non-linear transformation H (parameterized by W H,l ) on its input x l to produce its output y l . x 1 is the input to the network and y L is the network's output.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Second, the CSI algorithm selects inducing points in a single greedy pass using an approximate objective.
Sentence 2: instead of evaluating the change in the objective exactly, we use an efficient approximation based on a small number, z, of training points which provide information about the residual between the current low-rank covariance matrix (based on inducing points) and the full covariance matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In contrast, RSVD, which is equivalent to subspace iteration with a Gaussian random matrix, constructs a basis for A j 1 V 0 and then restricts A to this subspace to obtain the decomposition.
Sentence 2: more specifically, suppose that we select the top-k i eigenpairs of A ii and construct an ki 's and form an n ⇥ k orthonormal matrix ⌦ as where P i k i = k and denotes direct sum, which can be viewed as the sum of the subspaces spanned by U (i) ki .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our model has two novel components: (1) A domain-invariant feature self-reconstruction task is introduced to the seen/unseen class data, resulting in a simple linear formulation that casts ZSL into a min-min optimization problem.
Sentence 2: without any labels, the unseen class data has limited effect in overcoming the domain gap using existing transductive ZSL models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Any MBRL algorithm must select a class of model to predict the dynamics.
Sentence 2: our method to predict plausible state trajectories begins by creating P particles from the current state, s p t=0 = s 0 ∀ p. Each particle is then propagated by: s p t+1 ∼ f θ b(p,t) (s p t , a t ), according to a particular bootstrap b(p, t) in{1, . . . , B}, where B is the number of bootstrap models in the ensemble.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This leads to a sequential monomial approximations of the original SP formulation: at each iteration y (k) , we linearize both terms in Eq.
Sentence 2: despite the hardness of SP in general, the objective function in the MLE formulation of SPNs has a special structure, i.e., it is the ratio of two posynomials, which makes the design of efficient optimization algorithms possible.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In these applications there is a natural place where one might divide data into episodes: for type 1 diabetes treatment, one might treat each day as an independent episode, and for digital marketing, one might treat each user interaction as an independent episode.
Sentence 2: if the behavior and evaluation policies are both options-based policies, then the PDIS estimator can be exponentially more data efficient compared to using primitive behavior and evaluation policies.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Neural parsing methods [16,17] are grammar-like models for scene understanding, but use precomputed superpixels and thus also do not permit arbitrary region shapes.
Sentence 2: since there are an exponential number of subregions of an image, SFG-PARSE instead constructs a parse of the entire image for each production and reuses that parse for each of these subregions.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This strategy has not, to our knowledge, been applied either to multidimensional data or bounding-box prediction, as we do here.
Sentence 2: it is entirely possible there are errors in the labeling: for instance, there is little agreement in the climate community on a standard heuristic for capturing Extra-Tropical Cyclones (Neu et al., 2013); Atmospheric Rivers have been extensively studied in the northern hemisphere (Lavers et al., 2012;Dettinger et al., 2011), but not in the southern hemisphere; and spatial extents of such events not universally agreed upon.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then the margin condition (7) is satisfied if and only if there exists a constant C > 0 such that, for all ✏ > 0, (`, F ✏ , P ⇤ ) is ⌘-stochastically mixable for ⌘ = C✏ ( 1)/ .
Sentence 2: let ⌘ > 0 and suppose `is a loss such that its pseudolikelihood set e ⌘S is closed and pre-supportable.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To systematically monitor skin disease activity, clinicians use the TSS which is a quantitative score between 0 and 55 computed by evaluating skin thickness at 17 sites across the body (higher scores indicate more active skin disease).
Sentence 2: the joint distribution over y is a multivariate normal: where Σ DTM is a covariance matrix that depends on the times t 1:m (through design matrices B 1:m ) and representations x 1:m . Σ DTM is a block-structured matrix with m row blocks and m column blocks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: On-line learning algorithms, such as the Perceptron algorithm [17], the Winnow algorithm [14], and their many variants [16,6,13,10,2,9], are general methods for solving classification and regression problems that can be used in a fully incremental fashion.
Sentence 2: 1 The average hypothesis generates valid predictions whenever the decision space I is convex.
Relationship: neutral
Domain: NeurIPS
Sentence 1: provides an exact solution for the ground state of a 2D lattice Ising model without a ferromagnetic field [13,8,9,10] in O(N Computing a lower bound: At a given iteration, prior to adding a newly generated set of constraints we can compute the total residual constraint violation over all layers of hierarchy by ∆ = l (θ l + λ l + ω l−1 − ω l ) • z l . In the supplement we demonstrate that the value of the dual objective plus 3 2 ∆ is a lower-bound on the relaxed closest ultrametric problem in Eq 9.
Sentence 2: we optimize the dual of the objective in Eq 9 using an efficient column generation approach based on perfect matching.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As revealed by the recent literature findings [28], the deep features in standard CNNs must eventually transition from general to specific along the network, and the feature transferability decreases while the task discrepancy increases, making the features in higher layers f c7-f c8 unsafely transferable across different tasks.
Sentence 2: all three datasets are evaluated using DeCAF 7 [9] features for shallow methods and original images for deep methods.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To address this challenge, reweighted amplitude flow effecting suitable gradient directions from all data samples {(a i ; ψ i )} 1≤i≤m will be adopted in a (timely) adaptive fashion, namely introducing appropriate weights for all gradients to yield the update The reweighted gradient ∇ rw (z t ) evaluated at the current point z t is given as for suitable weights {w i } 1≤i≤m to be designed next.
Sentence 2: the losses (z; ψ i ) in (2) that are nonsmooth at points z will be eliminated, to prevent their contribution to the reweighted gradient update in (10).
Relationship: neutral
Domain: NeurIPS
Sentence 1: An important implication of Theorem 1 is that any iterative algorithm, such as EM or gradient ascent, that attempts to maximize the likelihood based on local updates cannot be globally convergent-that is, cannot converge to (near) globally optimal solutions from an arbitrary initialization.
Sentence 2: since the log-likelihood is bounded from above, this neighborhood must contain at least one maximum of the log-likelihood.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If we know that the ratio of the false positive and false negative costs is approximately θ : (1 − θ), it is reasonable to solve the following cost-sensitive SVM [17]: where the weight w i (θ) is defined as When the exact false positive and false negative costs in the test scenario are unknown [4], it is often desirable to train several cost-sensitive SVMs with different values of θ.
Sentence 2: we define w i (t) ∈ [0, 1], t ∈ N T as the weight of the i th instance for the t th task, where T is the number of tasks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Multiresolution Matrix Factorization (MMF) MMF is a recently introduced matrix factorization algorithm motivated by similar multiresolution ideas as the present work, but applied at the level of individual matrix entries rather than at the level of matrix blocks [31].
Sentence 2: it is clear from its form that the Nyström approximation is spsd preserving , so is augmented SPCA compression.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When the target conditional is close to all source ones, ↵ can be chosen to be very large and ✏ T is close to ✏.
Sentence 2: more details are presented in Appendix C. These results are non-trivial and important, as they provide a guarantee for an accurate and robust predictor for a commonly used loss function, the cross-entropy loss.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Approximation algorithms for this problem are essential since solving the problem exactly is NP-hard [12,14], even when k = 1 and A is a binary matrix.
Sentence 2: we allow the algorithm to output a matrix Although we do not obtain rank exactly k, many of the motivations for finding a low rank approximation, such as reducing the number of parameters and fast matrix-vector product, still hold if the output rank is O(k log(n/k)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We denote by ω and σ the mean and width of each Gaussian kernel, and we denote by h Finally, for ν njk = f (a njk ) we form a neural network that takes as input the score s njk , the binned variables h nj , which summarize the information of the scores (s njk : k = k), as well as the target observation x nj and the prior probability π nj .
Sentence 2: we report the approximate posterior probabilities in Table 3, for two query items (one from each type).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Additionally, this means that p(S) ≥ 2/3, so again with high probability, at least half of our m samples will lie in S. These first m /2 samples from S will be independent samples from (p|S), which is uniform, and therefore with 99% probability will pass the uniformity tester.
Sentence 2: from the above, we derive an algorithm that approximates p r to a small relative error: Lemma 2.3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A model is said to be walk-summable if for each pair of vertices s, t ∈ V , the absolute sum over all walks from s to t in G converges: Here, W(s → t) represents the set of all walks from s to t, and φ(s → t) denotes the absolute walk-sum 2 over this set.
Sentence 2: here, V 2 represents the set of all unordered pairs of vertices.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Sampling a trajectory over a long interval will take more time than over a short one, and to more clearly distinguish performance for large values of t end , we scale each ESS from the left plot with t end , the length of the interval, in the right subplot of figure 5.
Sentence 2: as this parameter varied from 0 to 1, the problem moved from sampling from the prior to a situation where the trajectory was observed (almost) perfectly at 10 random times.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A prototype chip was designed in a 0.35-µm CMOS technology and the fab-ricated chip generates an edge based image vector every 80 µsec, which is about 10 4 times faster than the software computation.
Sentence 2: a number of algorithms developed for robust image recognition so far [1]- [3] are mostly implemented as software systems running on general-purpose computers.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We can see from Figure 1(c) and 1(d) that our algorithm FLASH converges faster with larger step sizes for negative curvature descent, which validates our theories on third-order smoothness can be helpful in the nonconvex stochastic optimization.
Sentence 2: according to recent work by [34,5], one can extract the negative curvature direction by only using stochastic gradient evaluations, which makes the negative curvature descent approach more appealing.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Following [18], we introduce a small perturbation ζ > 0 to replace M 2,1 by i m i 2 2 + ζ, which is smooth and differentiable with respect to M . Apparently, i m i 2 2 + ζ is reduced to M 2,1 when ζ → 0.
Sentence 2: we evaluate the proposed method by applying it to the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort to examine the association between a wide range of imaging measures and two types of cognitive measures over a certain period of time.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Due to the size of the dataset, the analysis of [27] requires breaking the chain into several blocks, severing long range dependencies.
Sentence 2: ( 7), but with time indices restricted to the length L subchain y S : To compute these local beliefs, we use our current q(A), q(φ)-which have been informed by all previous subchains-to form π, A, p S = { p(y S |x S = k), ∀k, = 1, . . . , L}, with these parameters defined as in the batch case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Bayesian people tracking requires dynamical models in the form of transition densities in order to specify prediction distributions over new poses at each time instant (e.g., [11,14]); similarly, data-driven computer animation requires prior distributions over poses and motion (e.g., [1,4,6]).
Sentence 2: figure 1(a) depicts the graphical model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (ii) After learning (with plasticity at the bottom-up synapses (W PP 1,0 )), the network successfully predicts the new teaching signal, reflected on no distal 'error' (top-down and lateral interneuron input cancel each other).
Sentence 2: we postulate that the apical dendrite has an explicit error representation by simultaneously integrating top-down excitation and lateral inhibition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the algorithm guarantees a zero regret against the competitor with zero L 2 norm, then there exists a sequence of T vectors in X , such that the regret against any other competitor is Ω(T ).
Sentence 2: i built upon ideas of [19], but I designed my new algorithm as an instantiation of OMD, rather than using an ad-hoc analysis.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since there is no consensus on how to generate object tracking displays in the visual attention literature, we will assume simple linear dynamics, which can approximate prior experimental manipulations.
Sentence 2: the resulting accuracy surface is shown in Figure 2 -an apparent tradeoff can be seen, when objects move faster, they must be farther apart to achieve the same level of accuracy as when they move slower.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 4 Practical Aspects From now on we will drop the logarithm terms to simplify presentation.
Sentence 2: once the histogram is constructed, following Algorithm 1, we can view it as a set of h −d n = O(n 2d/(2+d) ) weighted data points a r , r ∈ {1, . . . , h −1 n } d associated with weights {n r }, where each data point a r is the center of cell B r as defined in Step 2 of Algorithm 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let K ∈ T and C be a cycle in G K . We denote by π For example, if the graph in Figure 1 is the adjacency graph of some K ∈ T and C is the cycle where the oriented cycles → C 1 , → C 3 and → C 5 are given above, and where we use the shortcut K ( → C j ) , where C j is the unoriented version of → C j .
Sentence 2: the matrix K is called the kernel of the DPP, and we write Y ∼ DPP(K).
Relationship: neutral
Domain: NeurIPS
Sentence 1: By Theorem 2.1 for kzc, C is a (k, z )-center solution to (P , w ) of cost at most 4 • 5L = 20L.
Sentence 2: the (1 + , 1 + )-bicriteria approximation ratio comes with a caveat: our algorithm has running time exponential in many parameters such as 1 , k, D and m (though it has no exponential dependence on n or z).
Relationship: neutral
Domain: NeurIPS
Sentence 1: This choice of notation was deliberate; one may define elic C := min{k : ∃ Γ ∈ E k ∩ C, ∃f, Γ = f • Γ} to be the complexity with respect to some arbitrary class of properties C. Some examples of interest might be elic E for expected values, of interest to the prediction market literature [8], and elic cvx for properties elicitable by a loss which is convex in r, of interest for efficiently performing ERM.
Sentence 2: while L must be concave, it may not be strictly so, thus enabling level sets which are potentially amenable to elicitation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: They proposed SDS MA and SDS OMP , and analyzed the approximation ratio using the coherence of the matrix A. Das and Kempe [10] introduced the concept of the submodularity ratio  Approximation ratio Running time Generalized sparsity SDS MA [22] m1ms M1Ms (1 − 1/e) [10] O((k + d)nT ) No SDS OMP [22] O Replacement Greedy [30] m2s Ms,2 O((n + ds)kT ) Yes and refined the analysis via the restricted isometry property [5].
Sentence 2: we approximate a data point y t with a sparse representation in atoms in X, where the approximation quality is measured by u.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Step size h allows us to quantify the rate of change of intersection if τ is increased from 0 to ∞, and since z t is decreasing, k r will evaluate to a high value for two points from the same subspace.
Sentence 2: without lost of generality assume that M is wholly divisible by h. Step size h is used to obtain the Difference of Intersection Kernel (DOIK) where indicates the set formed by the a-th to the b-th elements of θi .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The objective function in (15) fits naturally into the framework of (1), with Ω(α) − Ω(β) and constraints corresponding to M , and the rest terms to K. The entropy function Ω is convex wrt the KL-divergence, which is in turn distance enforcing wrt the 1 norm over the probability simplex [23].
Sentence 2: assume the proximal operator has been called #po number of times, then #pass := number of epochs so far We also compared with a "convex" approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is easy to control the trade-offs between the complexity of the recognizer network, the information capacity of the codes, and the robustness of the recognition towards different adversarial effects.
Sentence 2: in each case we show six markers: (1) -the marker corresponding to a bit sequence consisting of −1, (2) -the marker corresponding to a bit sequence consisting of +1, (3) and ( 4) -markers for two random bit sequences that differ by a single bit, ( 5) and ( 6) -two markers corresponding to two more random bit sequences.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that "separation condition" requirement refers to T 1 (x), T 2 (x) being small, so that eigenfunctions corresponding to the largest eigenvalues of convolution operator when applied to individual high density bumps are preserved in the case when convolution operator is applied to the mixture.
Sentence 2: it has been shown ( [SBY08a,SBY08b]) that when data distribution P X has clusters, for each high density region there is a unique representative eigenfunction of a convolution operator that takes positive values around the chosen cluster and is close to zero everywhere else.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A fast associative memory has several advantages when compared with the type of memory assumed by a Neural Turing Machine (NTM) , Neural Stack [Grefenstette et al., 2015], or Memory Network [Weston et al., 2014].
Sentence 2: this overcomes the objection that these models can only do recursion by storing copies of neural activity vectors, which is biologically implausible.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The compact and explicit polynomial form reveals important insights in the program semantics (e.g., the internal program loop that affects program execution time the most).
Sentence 2: condition 4 is a little bit tricky; it says that the irrelevant predictors (X S c ) are not very correlated with the "residuals" of E(Y ) after its projection onto X S . Condition 5 is always needed when considering LASSO's model selection consistency [26,28].
Relationship: neutral