sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: Given these definitions, the training in [4] can be interpreted as guided policy search for the MDP described in the previous paragraph.
Sentence 2: the variational distribution q provides a guide policy q(τ |x * ) over trajectories τ {z 0 , ..., z T , x * }: The primary policy p generates trajectories distributed according to: which does not depend on x * .
Relationship: entailment
Domain: NeurIPS
Sentence 1: Let I ′ be the set of non-zero columns of C ′ , and let H ′ be the column-normalized version of C ′ .
Sentence 2: column i 2 for all i ∈ I ′ , and H ′ i = 0 for all i / ∈ I ′ .
Relationship: entailment
Domain: NeurIPS
Sentence 1: . . , f n : [0, 1] → R may be nonconvex and the notation [n] denotes the set {1, 2, . . . , n}.
Sentence 2: our goal is to develop an algorithm that achieves an objective -close to the global optimal value for any > 0 with a complexity that scales along with the properties of f . we present an algorithm that simultaneously achieves the best known bounds when f i are convex and also for general f i , while scaling much better in practice than the straightforward approach when considering f used in robust estimation such as Huber Loss, Tukey's biweight function, and MCP.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox [12], models within our framework are stationary across steps of the graph sequence.
Sentence 2: our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure.
Relationship: entailment
Domain: NeurIPS
Sentence 1: . . , U m } ∈ C m (S) to be their common refinement.
Sentence 2: the clusters of U consist of those elements that are in the same clusters of both S and T . Formally, This result can be thought of as expressing a relationship between seperation and the lattice of partitions of S which will be important to our later robustness extension Lemma 6.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Their base operation is evaluating the proximal operator of a function, which involves solving a small convex optimization problem that often admits a closed-form solution.
Sentence 2: the proximal operator prox f (x 0 ) : R → R of a function is defined as If f is convex, the fixed points of the proximal operator of f are precisely the minimizers of f . In other words, prox f (x * ) = x * iff x * minimizes f . This fix-point property motivates the simplest proximal method called the proximal point algorithm which iterates x (n+1) = prox f (x (n) ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: In such settings, revenue sharing is a central part of running such a marketplace for the intermediary, and fixedpercentage revenue sharing schemes are often used to split the revenue among the platform and the sellers.
Sentence 2: such revenue sharing schemes require the platform to (i) take at most a constant fraction α of the revenue from auctions and (ii) pay the seller at least the seller declared opportunity cost c for each item sold.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Initialization: The α, β and γ weights are initialised in a bottom-up fashion on the decomposition tree -we initialise the weights of a vertex after we have initialised the weights of all its children.
Sentence 2: we first do a depth-first search of D starting from r: When we reach an edge (v, w) ∈ E(T ), if neither v or w is a leaf then we set β ab ((v, w)) ← θ (v,w),a,b otherwise assuming w is a leaf we set α a (v) ← 1 (dummy edge).
Relationship: entailment
Domain: NeurIPS
Sentence 1: To evaluate the performance of Neurify, we test it on nine models trained over five datasets for different tasks where each type of model includes multiple architectures.
Sentence 2: we evaluate on fully connected ACAS Xu models [16], three fully connected Drebin models [5], three fully connected MNIST models [21], one convolutional MNIST model [42], and one convolutional self-driving car model [2].
Relationship: entailment
Domain: NeurIPS
Sentence 1: Let R be a ⌫-selfconcordant barrier for K. Then, for ⌘k  12d , the regret of OPTIMISTICBCO can be bounded as follows: (k + 1) 2 .
Sentence 2: for ⌘ = T 8/13 d 5/6 , = T 5/26 d 1/3 , k = T 1/13 d 5/3 , the following guarantee holds for the regret of the algorithm:  This work was partly funded by NSF CCF-1535987 and IIS-1618662 and NSF GRFP DGE-1342536.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Suppose we have a probability distribution p b (x) = f b (x)/Z b defined on a space X , where f b (x) can be computed efficiently for a given x ∈ X , and we are interested in estimating the partition function Z b . Annealed importance sampling (AIS) is an algorithm which estimates Z b by gradually changing, or "annealing," a distribution.
Sentence 2: one must specify a sequence of K + 1 intermediate distributions p k (x) = f k (x)/Z k for k = 0, . . . K, where p a (x) = p 0 (x) is a tractable initial distribution, and p b (x) = p K (x) is the intractable target distribution.
Relationship: entailment
Domain: NeurIPS
Sentence 1: On the other hand, [12] shows that the rate n /( +p) is often asymptotically optimal in a minmax sense.
Sentence 2: the latter is the case for H = W m 2 (X), f 2 W s 2 (X), and s 2 (d/2, m], that is, when using a Sobolev space as the underlying RKHS H, then all target functions contained in a Sobolev of lower smoothness s > d/2 can be learned with the asymptotically optimal rate n 2s 2s+d .
Relationship: entailment
Domain: NeurIPS
Sentence 1: In the full version of the paper, for the specific problem of portfolio selection, where f t (x) = − log(r t • x), we give a faster implementation whose per iteration running time is independent of the number of iterations, using the more sophisticated "online Newton method" of [HKKA06].
Sentence 2: we have the following result: Theorem 4.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The proposed iFDM in Figure 1a can be particularized to resemble some other models that have been proposed in the literature.
Sentence 2: we recover: i) the iFHMM in [23] by choosing the state space X = {0, 1}, x tm = s tm and L = 1, ii) the ICA iFHMM in [23] if we set X = R, L = 1 and assume that p(x tm |s tm = 1, x (t−1)m , s (t−1)m ) = p(x tm |s tm = 1) is a Gaussian distribution, and iii) a BNP counterpart of the LDS [9] with on/off states by assuming L = 1 and X = R, and letting the variables x tm be Gaussian distributed with linear relationships among them.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We build on the proof of this result to show that the class of n-bidder, m-item MBARPs has a pseudo-dimension of O m 3 log n . We note that when we analyze the class of MBARPs, we assume additive reserve prices, rather than bundle reserve prices.
Sentence 2: each item has its own reserve price, and the reserve price of a bundle is the sum of its components' reserve prices, as opposed to each bundle having its own reserve price.
Relationship: entailment
Domain: NeurIPS
Sentence 1: With this in mind, we conducted a preliminary experimental evaluation of Algorithm 1, implemented using a popular algorithm for learning decision trees in place of the required ERM oracle.
Sentence 2: we use the J48 algorithm from Weka v3.6.2 (with default parameters) to select the hypothesis h k in each round k; to produce the "alternative" hypothesis h ′ k , we just modify the decision tree h k by changing the label of the node used for predicting on x k . Both of these procedures are clearly heuristic, but they are similar in spirit to the required optimizations.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Our empirical results show that in practice the constants inside the Θ-notation are significantly tighter than the theoretical proof might suggest, and in fact feature hashing performs well for a larger scope of vectors.
Sentence 2: for a synthetic set of generated bit-vectors, we show that whenever ε 2 δ the constant hidden by the Θ-notation is at least 0.75 (except for very sparse vectors, i.e.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Beyond Ω min 1/γ, n/V queries, , and hence, Theorem 3.2 implies that the misclassification rate of 4 From Answering Queries to Model-agnostic Private Learning In this section, we build on our algorithm and results in Section 3 to achieve a stronger objective.
Sentence 2: we bootstrap from our previous algorithm an ( , δ)-differentially private learner that publishes a final classifier.
Relationship: entailment
Domain: NeurIPS
Sentence 1: A key aspect of our framework is that the conditional posteriors of all the model parameters are available in closed form using data augmentation strategies that we will describe below.
Sentence 2: since we model binary label matrix as thresholded counts, we are also able to leverage some of the inference methods proposed for Bayesian matrix factorization of count-valued data [27] to derive an efficient Gibbs sampler for our model.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Extending the adaptive feed-forward layer to RNNs, we presented an adaptive LSTM that significantly increases model capacity and statistical efficiency while being more robust to hyper-parameters.
Sentence 2: we obtain new state of the art results on the Penn Treebank and the WikiText-2 word-modeling tasks, using ~20-30% fewer parameters and converging in less than half as many iterations.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In either case we denote u i = f (x i ), and in LIN:LIN also v i = g(x i ), and learn by attempting to minimizing the objective in (3), where (•) is again a continuous loss function such as the square root of the logistic.
Sentence 2: we learn by optimizing the problem (3) with the additional constraint U = sign(W q X), and possibly also V = sign(W d X) (for LIN:LIN), where We optimize these problems by alternatively updating rows of W q and either rows of W d (for LIN:LIN ) or of V (for LIN:V ).
Relationship: entailment
Domain: NeurIPS
Sentence 1: The survival function S(t) gives us the probability a patient survives up to time t, while the hazard function λ(t) gives us the instant risk of patient at time t. We define a Gaussian process prior over the hazard function λ.
Sentence 2: we choose λ(t) = λ 0 (t)σ(l(t)), where λ 0 (t) is a baseline hazard function, l(t) is a centred stationary Gaussian process with covariance function κ, and σ is a positive link function.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The U-Tree algorithm retains the subtree of distinctions i at a leaf Lj if the sum of the KS statistical differences over the fringe nodes F(Lj , i) of the subtree is (1) larger than the sum of the KS differences of all other subtrees, and (2) exceeds some threshold 8.
Sentence 2: the tree is extended from leaf L j with a subtree i of new distinctions if for all subtrees m -=I-i: and Whenever the tree is extended, the action values of the previous leaf node are passed on to the new leaf nodes.
Relationship: entailment
Domain: NeurIPS
Sentence 1: . . , ω kN , for k = 1, . . . , K. These expectations are available in closed form and can thus easily be computed.
Sentence 2: the expectation of each Pólya-Gamma variable ω kn is very efficient to compute and is available in closed form [20] E The M-step involves a maximization w.r.t.
Relationship: entailment
Domain: NeurIPS
Sentence 1: But we did not consider this to be a good choice.
Sentence 2: consider making the helicopter fly in the increasing -direction, so that $ ¤£ ¡ £ $£ ¡ §¦ p£ ¡ £ ( starts off as $ F ¡ ¡ ¡ ( (say), and has its first coordinate £ slowly increased over time.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For example, if X 1 and X 2 are independent given X 3 , X 4 , and We cast the problem of learning the structure of a deep neural network as a problem of learning the structure of a deep (discriminative) probabilistic graphical model, G dis .
Sentence 2: a graph of the form where " " represent a sparse connectivity which we learn, and "→" represents full connectivity.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Describing the contents of images is useful for automated image captioning and conversely, the ability to retrieve images based on natural language queries has immediate image search applications.
Sentence 2: in this work we are interested in training a model on a set of images and their associated natural language descriptions such that we can later rank a fixed set of withheld sentences given an image query, and vice versa.
Relationship: entailment
Domain: NeurIPS
Sentence 1: For the Ising model on the grid, the critical edge parameter for high-temperature is .
Sentence 2: we are in high-temperature if and only if θ ≤ θ c , and we can reject the null hypothesis if the MPLE estimate θ > θ c . To generate departures from the null hypothesis, we give construction parameterized by τ ∈ [0, 1].
Relationship: entailment
Domain: NeurIPS
Sentence 1: First, we note that there is an inverse relationship between the tail exponent q in (H2) and the decay rate β of the algorithm's step-size sequence γ n ∝ n −β .
Sentence 2: higher values of q imply that the noise in the players' observations is smaller (on average and with high probability), so players can be more aggressive in their choice of step-size.
Relationship: entailment
Domain: NeurIPS
Sentence 1: It is interesting to see that several well-known nonparametric estimators for classification and regression can be seen as special cases of this estimator (or a slightly more general form) for different choices of the output space, its metric and the loss function.
Sentence 2: the approach shows a certain analogy of a generalization of regression into a continuous space (manifold-valued regression) and regression into a discrete space (structured output learning).
Relationship: entailment
Domain: NeurIPS
Sentence 1: These can be uniquely defined as the solutions of the following Bellman equations: Now, consider the trajectory {(x t , a t )} underlying a learning agent, where x 1 is randomly chosen from P 0 , and define and π t (a|x) = P[a t = a|u t−1 , x t = x].
Sentence 2: π t denotes the policy followed by the agent at time step t (which is computed based on past information and is therefore random).
Relationship: entailment
Domain: NeurIPS
Sentence 1: Given the network polynomial f , we can answer any query with respect to the belief network.
Sentence 2: let e be an instantiation of some network variables, and suppose we want to compute the probability of e. W e can do this by simply evaluating the polynomial f while setting each evidence indicator λ x to 1 if x is consistent with e, and to 0 otherwise.
Relationship: entailment
Domain: NeurIPS
Sentence 1: We treat the ambiguity of e as a hidden class z over e and make use of the query log as a data source for mining the relationship among e, w and z.
Sentence 2: the query log can be viewed as a multi-class, multi-label and multi-instance corpus {(X n , Y n )} n=1,2,...,N , in which each pattern X corresponds to a named-entity e and is characterized by a set of instances {x m } m=1,2,...,M corresponding to all the contexts {w m } m=1,2,...,M that co-occur with e in queries, and the label Y contains all the ambiguities of e. Our data was based on a snapshot of answers.yahoo.com crawled in early 2008, containing 216563 queries from 101 classes.
Relationship: entailment
Domain: NeurIPS
Sentence 1: ( 6), for its ease of implementation and practical effectiveness [35].
Sentence 2: at iteration t, let β t c be the current value of β c . We compute f (β c )'s subgradient s t , then perform the following update, where the max( ) function implements the projection operation such that the update does not fall outside of the feasible region β c ≥ 0.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In order to allow the time point at which the goals are achieved to be influenced by the optimization, we will re-frame the goal driven part of the problem in a canonical time and in addition to optimizing the controls, also optimize the mapping from canonical to real time.
Sentence 2: we introduce into the problem defined by ( 1) & ( 2) the canonical time variable τ with the associated mapping with θ as an additional control.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To optimize (7), we utilize Monte Carlo methods to approximate expectations and stochastic gradient descent (SGD) for parameter optimization.
Sentence 2: the gradients can be expressed as in the TSBN model, if we define vmt = σ(w 2m h t + w 4m v t−1 + c m ) and ĥjt = σ(u 1j h t−1 + u 2j v t + u 3j v t−1 + d j ), the gradients for w 2m and u 2j can be calculated as Other update equations, along with the learning details for the TSBN variants in Section 2.3, are provided in the Supplementary Section B.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In particular, such an algorithm would imply a breakthrough result for the problem of learning k-juntas (functions that depend on only k n input variables; it is not known how to learn ω(1)-juntas in polynomial time).
Sentence 2: we present an algorithm and a set of natural conditions such that any sparse polynomial f satisfying these conditions can be learned from random examples in time polynomial in n and 2 s . any f whose coefficients have been subjected to a small perturbation (smoothed analysis setting) satisfies these conditions (for example, if a Gaussian with arbitrarily small variance is added independently to each coefficient, f satisfies these conditions with probability 1).
Relationship: entailment
Domain: NeurIPS
Sentence 1: We established nearly tight finite-sample convergence guarantees showing that NNQL can accurately estimate optimal Q function using nearly optimal number of samples.
Sentence 2: our results state that the sample, space and computational complexities of NNQL scale polynomially (sometimes linearly) with the covering number of the state space, which is continuous and has uncountably infinite cardinality.
Relationship: entailment
Domain: NeurIPS
Sentence 1: In this way, each sub-model could independently identify their optimal sub-assignments.
Sentence 2: for example, we can use the parameters: Since sub-models M i and M j become independent after relaxing the single equivalence constraint X i ≡ X j , computing these parameters is sufficient to reconstruct the MAP solution for the original model M. we have that θ( We propose then that the parameters of a compensation, with MAP values c-map(.
Relationship: entailment
Domain: NeurIPS
Sentence 1: But unlike previous works, we use minibatches as a theoretical tool to improve convergence rates of both nonconvex PROXSVRG and PROXSAGA.
Sentence 2: by carefully selecting the minibatch size, we can improve the IFO complexity of the algorithms described in the paper from O(n/✏) (similar to PROXGD) to O(n 2/3 /✏) (matching the smooth nonconvex case).
Relationship: entailment
Domain: NeurIPS
Sentence 1: As in [7], we use contrast filters that have spatial characteristics and contrast response properties closely mirroring well-known characteristic receptive-fields of LGN neurons [9].
Sentence 2: we use a bank of second-order Gaussian derivative filters that span multiple octaves in spatial scale, that have peak sensitivity approximately inverse to filter size and that have contrast gain properties independent of size.
Relationship: entailment
Domain: NeurIPS
Sentence 1: The idea here is to allow the learner to preemptively "guess" the gradient at the next step and optimize for this in the FTRL update.
Sentence 2: if e g t+1 is an estimate of the time t + 1 gradient g t+1 based on information up to time t, then the learner should play: This optimistic FTRL algorithm admits the following guarantee: Lemma 4 (Lemma 1 [Rakhlin and Sridharan, 2013]).
Relationship: entailment
Domain: NeurIPS
Sentence 1: In order to adapt one domain to the others, one approach is to consider a penalty proportional to the distance between each distribution and the weighted mean of the rest.
Sentence 2: let P s be the distribution over data points x in domain D s , and P /s = 1 S 1 P S s 0 =1 w ss 0 P s 0 the distribution of data from all other domains D ws /s .
Relationship: entailment
Domain: NeurIPS
Sentence 1: The mGP provides a flexible framework for characterizing the dependence structure of real data, such as the examined MEG recordings, capturing certain features more accurately than previous models.
Sentence 2: the mGP provides a hierarchical functional data analysis framework for modeling (i) strong, locally smooth sharing of information, (ii) global long-range correlations, and (iii) abrupt changes.
Relationship: entailment
Domain: NeurIPS
Sentence 1: An event E occurs in the history Φ i , written Φ i E, if and only if some component occurs in that history: ∃e ∈ E : Φ i e. Events can therefore be thought of disjunctively.
Sentence 2: they specify a set of possible state-action transitions from a Dec-POMDP, local to one of its agents.
Relationship: entailment
Domain: NeurIPS
Sentence 1: ( 10) with respect to f is equivalent to minimizing serves as a good critic of f (x) when it makes the cost g(x){µ w (x)f (x) − 2µ z (x)} larger for x at which f makes a larger error |µ w (x)f (x) − 2µ z (x)|.
Sentence 2: g maximizes the objective above when g(x) = µ w (x)f (x) − 2µ z (x) for any f , and the maximum coincides with the least-squares objective in Eq.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Since we never know the real property of the (unknown) probability space, it is more likely the requirement on the probability space for the consistency with the top-k true loss can be satisfied than that for the top-l (l > k) true loss.
Sentence 2: it is risky to assume the requirement for the permutation-level 0-1 loss to hold.
Relationship: entailment
Domain: NeurIPS
Sentence 1: . . , y N } is a probability measure on 2 Y , the set of all subsets of Y. P is called a determinantal point process (DPP) if there exists a positive semidefinite matrix K indexed by the elements of Y such that if Y ∼ P then for every A ⊆ Y, we have Determinantal Point Process: Here K A = [K ij ] yi,yj ∈A is the restriction of K to the entries indexed by elements of A, and we adopt det(K ∅ ) = 1.
Sentence 2: we will refer to K as the marginal kernel, as it contains all the information needed to compute the probability of including any subset A in Y ∼ P. A few simple observations follow from Equation (1): the diagonal of K gives the marginal probabilities of inclusion for individual elements of Y, and the off-diagonal elements determine the (anti-) correlations between pairs of elements: large values of K ij imply that i and j tend not to co-occur.
Relationship: entailment
Domain: NeurIPS
Sentence 1: Assumption A holds with κ = 0, one can easily verify that for n ≥ s there exists a filter See [15, Appendix C] for the proof.
Sentence 2: this implies that x can be recovered efficiently from observations (1): if instead of the filtering problem we were interested in the interpolation problem of recovering x t given 2n + 1 observations y t−n , ..., y t+n on the left and on the right of t, Assumption A would imply a kind of simplicity of x.
Relationship: entailment
Domain: NeurIPS
Sentence 1: While the ✓ (c) j⌫ 0 is drawn as in (6), assigning ✓ ji } are executed as they would be in ( 4) and ( 5), without an MH step.
Sentence 2: a construction like ( 6) is used to assign elements of {✓ ⇤ i } to spikes, but after this step the update equations for {U (c) ji } are implemented as in the original (conjugate) model.
Relationship: entailment
Domain: NeurIPS
Sentence 1: To address this issue, we propose a hybrid optimization scheme.
Sentence 2: for a small constant ǫ > 0, if is not empty, we switch the iteration to the following gradient descent step (GD-step): where α is a step size chosen by the following line search procedure: for constants α 0 > 0, β, γ ∈ (0, 1) and m = 0, 1, • • • , find the smallest integer m with α = α 0 β m such that the following inequality holds: The detailed steps of the algorithm are presented in Algorithm 1.
Relationship: entailment