sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: That paper demonstrated that upper-confidence-bound (UCB) exploration schemes for concurrent reinforcement learning (concurrent UCRL), such as those discussed in [15,4,16], fail to satisfy the diversity property due to their deterministic nature.
Sentence 2: in concurrent UCRL, Thompson resampling and seed sampling, at each time t k,m , the agent k generates a new MDP M k,m based on the data gathered by all agents up to that time, computes the optimal policy π k,m for M k,m and takes an action a k,m = π k,m (s k,m−1 ) according to the new policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Specifically, we calculate a sequence of {f  i } n i=1 , and use kS t U > f tB k 2 n to approximate the bias term, where , B is a positive integer.
Sentence 2: in this section, we first derive the null limit distribution of (standardized) D n,t as a standard Gaussian under mild conditions, that is, we only require the total step sizes ⌘ t goes to infinity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, this may be achieved by solving a linear system of equations [3,20] involving the Laplacian, and a solution may be computed in O(|E| log O(1) n) time [18], where E is the edge set.
Sentence 2: we present experiments on two web-spam classification tasks, one of which includes a graph with 400,000 vertices and more than 10,000,000 edges.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While restricted to discrete states, [2] provides an important insight that we exploit in this work: only a finite number of partitionings of the observation space are required to distinguish between the optimal conditional policy over a finite set of belief states.
Sentence 2: the Γ h in this optimal h-stage-to-go value function can be computed via Monahan's dynamic programming approach to value iteration (VI) [4].
Relationship: neutral
Domain: NeurIPS
Sentence 1: To relate this to current PoE models, if λ T e φ(•) were replaced with a log Student-t function then this FRAME model would take the same form as the Product-of-Student-t formulation of [12].
Sentence 2: we model the joint probability of population spiking times and 2D hand position and show that the likelihood of test data under our model is significantly higher than under other models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These inhibitory patterns, which we call shadow patterns, are activated after the excitatory patterns fire, but have no special in-pattern connectivity or structured projections onto other patterns.
Sentence 2: the maximal load of our system is determined in terms of the available synaptic resources, and is proportional to the size of the excitatory population, N E . For the parameters used here it turns out to be P=0.06N E . This limit was estimated by a combinatorial argument of synaptic availability, and shown to be realized by simulations.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While the ranking from recursive independent component elimination did not reveal any evidence of an overwhelming contribution from artefacts related to muscle activity, it is not possible to rule out completely the involvement of such artefacts-possibly the only way to be sure of this is to implement the interface with locked-in patients, preparations for which are underway.
Sentence 2: there is considerable motivation to add to the palette of available BCI paradigms by exploring EEG signals that occur in response to auditory stimuli-a patient's sense of hearing is often uncompromised by their condition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that this is a special case of the class of methods studied in [6] (which considers more general projections) that leads to non progressive regret bounds, and this is the method of significant current interests [3,8].
Sentence 2: proposition 1 Let f j ∈ R n be a set of fixed vectors (j = 1, . . . , M ), and assume that q j ≥ 0 with j q j = 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 2 is called the upper bound on the variance of stochastic gradients [26].
Sentence 2: there is still an open question: whether e O(n ^✏ 2 + ✏ 3 ^n1/2 ✏ 2 ) is the optimal gradient complexity for finite-sum and stochastic nonconvex optimization problem?
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each x i ∈ D compute the Jacobian of the last layer representation J (K) (x i ) = ∂h (K) ∂x (x i ) and its SVD 1 .
Sentence 2: we will show record-breaking improvements by using TangentProp for fine tuning CAE-pre-trained deep neural networks.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In fact, when we consider the "worst" approximation which outputs y with the smallest score, its approximation error equals to the exact inference since h(x, w) = h -(x, −w).
Sentence 2: solving the "arg max" operation is essential for training and testing structured prediction models, and it is also one of the most time-consuming parts due to its combinatorial natural.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let O = S 1 ∩ S 2 be the indices for which both sensors are available, and By using the samples in S 1 and S 2 as two independent training sets, we may obtain two separate classifiers (denoted w 1 and w 2 ).
Sentence 2: by treating Υ( w) (the expectation of Γ(λ)) as deterministic, we obtain an evidence-type approximation [14]  , where p i is the (m − 1)-dimensional vector computed from (1), the c-th element of which indicates the probability that sample x i belongs to class c. Now let x * ∈ D U be an unlabelled sample and y * its label.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If f and H are conjugate, we can analytically compute the marginal likelihood of the K + 1st state, but this can also be approximated by Monte Carlo sampling for non-conjugate likelihoods -see Neal [2000] for a more detailed discussion of this argument.
Sentence 2: the key to constructing a generic, truncation-free sampler for the iHMM to resample the latent states, s 1:T , is to note that the finite number of particles in the sampler are "localized" in the latent space to a finite subset of the infinite set of possible states.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Intuitively the evaluation function must combine distances between the query trajectories and trajectories generated by the latent target policy.
Sentence 2: the disagreement measure is g = (ξi,ξj ) P (ξ i |θ i , s 0 , K)P (ξ j |θ j , s 0 , K)f (ξ i , ξ j ), which we estimate via sampling a set of K length trajectories from each policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In (Garrigues and Olshausen, 2010) the coefficients were given by a Laplacian scale mixture prior, leading to multiplicative modulation, as in this work.
Sentence 2: boltzman machines (Ackley et al., 1985) have a similar term, but the z and the inference are stochastic, e.g.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let ψ z m (i, σ) be the posterior probability density of the rescaled data-dependent posterior distribution Q over the classifier space with respect to the volume measure P. We can now replace δ for this bad event by the delta of the Occam's hammer defined as: where ln + denotes max(0, ln), the positive part of the logarithm.
Sentence 2: occam's hammer work by bounding the probability of bad event defined as follows.
Relationship: neutral
Domain: NeurIPS
Sentence 1: by using LfD to find initial policy parameters.
Sentence 2: in many problems, we do not have access to the exact Bellman operator T π , but only to samples In this case, one might want to use the empirical Bellman error It is known, however, that this is a biased estimate of the Bellman error, and does not lead to proper solutions [14].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given a p n ⇥ p n binary image x 0 2 {+1, 1} n , we generate a corrupted version of the same image y 2 {+1, 1} n . We then try to denoise y by maximizing the following objective function: U (x) = X (i,j)2E x i x j + ✓ 0 X i2V y i x i , (4.1) U and N represent uniform and normal distributions.
Sentence 2: the dimension of the above optimization problem is O(r P m `=1 |R `|2 ), which is O(nr) if the regions have bounded size; this will be the case in our implementation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: From here we can see that if we let L go to infinity and set k(n) = λ −n , 0 ≤ λ ≤ 1, then we obtain the λ-return estimator in equation ( 4), since .
Sentence 2: this leads to TD γ for episodic tasks (given in Algorithm 1), which eliminates the eligibility trace parameter λ.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As long as the eigenvalues of the blocks are different each eigen-vector will have non-zero values only in entries corresponding to a single block/cluster: where x (c) is an eigenvector of the sub-matrix L (c) corresponding to cluster c. However, as was shown above, the eigenvalue 1 is bound to be a repeated eigenvalue with multiplicity equal to the number of groups C. Thus, the eigensolver could just as easily have picked any other set of orthogonal vectors spanning the same subspace as X's columns.
Sentence 2: it highlights the different patterns of distribution of eigenvalues for different data sets.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We focus on convex optimization problems [2] of the form minimize f (x) subject to c(x) ≤ 0, where c(x) is a vector of inequality constraints, f (x) and c(x) have continous partial derivatives, and measurements y k of the gradient at x k are noisy.
Sentence 2: careful analysis [7] has shown that poor conditioning is not the problem-rather, it is a deficiency in the search direction.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, this positive definite ⌃ can be seen to satisfy our Condition (C3), since each row has only 4 non-zeros.
Sentence 2: for example, consider ⌃ where ⌃ SS = 0.95I 3 + 0.051 3⇥3 for a matrix 1 of ones, ⌃ SS c is all zeros but the last column is 0.41 3⇥1 , and .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each rule r is of the form f < v, where f ∈ f i and v is a value for f . The vector C is used during classification only when the corresponding node has one or more ∅ children.
Sentence 2: the theory we present here holds for any hypothesis, input and output space that may be handled by a computer with infinite resources (see [11; 12] for more precise descriptions).
Relationship: neutral
Domain: NeurIPS
Sentence 1: If the binary classification learning algorithm outputs scores that are probability estimates, they do not satisfy the first requirement because the probability estimates are all between 0 and 1.
Sentence 2: for this reason, we propose an algorithm analogous to the Hastie-Tibshirani method presented in the previous section to find the best approximate probability estimates pi (x) such that the Kullback-Leibler distance between rb x and r b x is minimized.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the logistic bandit, previous bounds for Thompson sampling [7] and upper-confidence-bound algorithms [5] scale linearly with sup x φ (x)/ inf x φ (x), where φ is the logistic function φ(x) = e βx /(1 + e βx ).
Sentence 2: even for problems with infinite action sets, like the linear bandit with a polytopic action set, Thompson sampling is known to obey gracious regret bounds [6].
Relationship: neutral
Domain: NeurIPS
Sentence 1: The L 1 -norm provides a convenient way of measuring such a distance, leading to the classical AUC criterion (AUC standing for area under the ROC curve): The popularity of this summary quantity arises from the fact that it can be interpreted in a probabilistic fashion, and may be viewed as a distance between the locations of the two distributions.
Sentence 2: for any pair of distributions (G, H), the centered random variable √ N {U n1,m1 (s) − AUC(s)} is asymptotically normal with limit variance σ 2 s (G, H) = Var(H s (s(X + 1 )))/p+Var(G s (s(X − 1 )))/(1−p) under P (G,H) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The resulting algorithm enjoys essentially the same regret bound, and can be implemented efficiently whenever efficient sampling is possible from the resulting distribution.
Sentence 2: then, there exists an algorithm such that for any T > 0, knowing T , the regret satisfies by choosing ↵ = 1/(T L), we have We note in passing that the the dependence of the algorithm on the time horizon T can be alleviated, using, for example, the doubling trick.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We use a linear combination of the reconstruction error for 'input', 'conv1_2', 'conv2_2', 'conv3_2', 'conv4_2' and 'conv5_2' layers of VGG-19; {α l } are updated online during training to normalise the expected contribution from each layer as in [4].
Sentence 2: this generalises significantly from the training examples, which only consist of pairs of digits sampled from the same house number instance, sharing a common style.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Several existing API methods [4,5] can provide both local optimality guarantees and global guarantees under strong assumptions regarding the way samples are generated (e.g., access to a reset distribution that is similar to the optimal policy's state distribution).
Sentence 2: 1 in high level follows GPS's iterative procedure of alternating reactive policy improvement and MBOC, the main difference between Alg.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 4.1), a greedy but not unreasonable choice is to set λ A (x N (A) ) to be the current Monte Carlo estimate of the marginal p(x Happily, the number of terms in ( 15) is now on the order of the number of the particles.
Sentence 2: mean field remains a popular tool for statistical inference, mainly because it applies to a wide range of problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Figure 1 (f) is a zoomed plot of this region and shows that the SD and CQ tests commit too many false positives at low thresholds.
Sentence 2: for example, when thresholding p-values at 0.01, SD has an actual FPR of 0.03, and an even more excessive FPR of 0.02 when thresholding at 0.001.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that although H(n i ) is only an upper bound on the statistical error, Bottou and Bousquet remark "it is often accepted that these upper bounds give a realistic idea of the actual convergence rates" [BB07], in which case balancing the sub-optimality with H(n i ) asymptotically minimizes the total error.
Sentence 2: instead of choosing new points from a static training set, such as in DYNASAGA, STRSAGA chooses new points from the dynamically changing buffer Buf.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Subsequently, a semidefinite relaxation of the original problem was presented which does not suffer from local minima.
Sentence 2: finding the dual leaves us with the following min max saddle point problem that will be subsequently relaxed and transformed into a semidefinite program: where 1 is a vector of ones, y is a vector of the labels, Y = diag( y) is a matrix with the labels on its diagonal with zeros elsewhere, and X is a matrix with x i in the ith column.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We are interested in whether our method can successfully capture the nonlinear property of this pendulum data.
Sentence 2: for our SSM, the traditional sampling importance resampling (SIR) particle filter will introduce the unnecessary computational load due to the fact that (5) in the SSM is a linear structure given θ t . This inspires us to apply a more efficient marginalized particle filter (also called Rao-Blackwellised particle filter) [9,11,12,13] to deal with the estimation problem by combining Kalman filter into particle filter.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that in both cases the (dense) population firing rate λ = m λ m (x) will be given by λ = √ 2πpφ/|∆θ|, where ∆θ is the separation between neighbouring tuning centres θ m . The Ornstein-Uhlenbeck (OU) process controlled by a process U t is given by the SDE Equation (7) can then be solved by simulating the dynamics of Σ s . This has been considered extensively in [13] and we refer to the results therein.
Sentence 2: we present examples that show two possible reasons for different optimal coding strategies in estimation and control.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A simple argument shows that the family of continuous functions with compact support is no longer dense in L 1 in infinite-dimensional spaces.
Sentence 2: we show that by the structure of the construction, combined with the packing and covering properties of γ-nets, we have that in any γ-net, the total measure of all these "bad" cells goes to 0 when γ → 0, thus yielding a consistent classifier.
Relationship: neutral
Domain: NeurIPS
Sentence 1: GBN significantly outperforms the state-of-the-art algorithm on Q 1 2 (we obtain the p-values of the paired t-tests for all the above differences on the test sets of queries, all these values are less than 0.005).
Sentence 2: this accuracy gives the required accuracy δ of the inexact first-order oracle for f (ϕ) on each step of the inner cycle of the Algorithm 2.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is known from Vapnik's cross-validation bound in [11] (Theorem 10.7) that by using the large margin idea alone, one can derive an expected misclassification error bound that is of the order O(l/n), where the constant is margin dependent.
Sentence 2: we first consider the following inequality which follows from the definition of w. (A):  It is well-known that every bounded sequence in a Hilbert space contains a weakly convergent subsequence (cf.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , a M }, and each latent vector is subject to a ∼ N H (0, I H ).
Sentence 2: we assume that the prior covariance matrices C A and C B are diagonal and positive definite, i.e., Without loss of generality, we assume that the diagonal entries of the product C A C B are arranged in the non-increasing order, i.e., c Throughout the paper, we denote a column vector of a matrix by a bold smaller letter, and a row vector by a bold smaller letter with a tilde, namely, The Bayes posterior is written as where is the marginal likelihood.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We can write the gradient as: For a plasticity rule to be biologically plausible it must be local, so only information encoded in the states of the pre-synaptic j and the post-synaptic i neurons must be considered to update ǫ ij .
Sentence 2: fluctuations around the reached state, slightly above η = 1, are approximately one order of magnitude bigger than for κ = 0.01.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Royer and Wright [17] proposed an algorithm that utilizes the negative gradient direction, the negative curvature direction, the Newton direction and the regularized Newton direction together with line search in a unified framework, and also analyzed the time complexity of a variant with inexact calculations of the negative curvature by the Lanczos algorithm and of the (regularized) Newton directions by conjugate gradient method.
Sentence 2: lemma 3 provides a similar guarantee to Lemma 2 and can be used to derive a similar convergence to Theorem 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To emphasize the dependence of the function r u (t) on τ u , we will also write r u (t) as r u (t|τ u ).
Sentence 2: for a fixed set S i , as time t increases, the cumulative number of events observed grows accordingly for that f (S i , t) is a continuous monotonic function over time; for a given time t, as the set S i changes to another set S j , the amount of coverage over domain U may change and hence can result in a different cumulative intensity.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Experimental results have shown that this model outperforms the standard tfidf bag of words model on a well known data set.
Sentence 2: since uc never occurs in d and Pu-+x ~ pv-+x, the u --+ x Fisher score entry for a document d becomes tf( ux, d) The Fisher kernel is subsequently defined to be k(d,d') = UJrIUd', where Ud is the Fisher score vector with ux-component a~n P( d) and I = Ed[UdUdTJ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unfortunately, traditional VP detectors tend to fail in the presence of clutter, which our images exhibit to a large extent, for example generated by shadows.
Sentence 2: hence, we have with s the index for the parking spot location within a parking area and Here, c p , π m and Σ m are defined as above, while µ m = µ m (s, l, R) ∈ R 2 is the coordinate of the parking spot location in bird's eye perspective (see Fig.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The key modification is to use (10) to show that the effect of the noise is asymptotically negligible so that for large n, This is done by separately considering the components of w in the span of the vectors a j for j ∈ I true and its orthogonal complement.
Sentence 2: this "genie" algorithm is identical to the regular OMP method in Algorithm 1, except that it runs for precisely k iterations as opposed to using a threshold µ for the stopping condition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Previous analyses of EM only established such results for specific methods of initializing EM (e.g., Dasgupta and Schulman, 2007;Balakrishnan et al., 2014); our results show that they are not really necessary in the large sample limit.
Sentence 2: sample-based EM iteratively updates its estimate of θ according to the following equation: where y 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that since in our application all training facts are ground atoms, we only make use of the proof success score ⇢ and not the substitution list of the resulting proof state.
Sentence 2: subsequently, we predict a ranking of every test fact and its corruptions to calculate MRR and HITS@m. Results for the different model variants on the benchmark KBs are shown in Table 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Before presenting our theoretical analysis, an important special case to discuss is ν = 1, which corresponds to a deterministic actor-critic method.
Sentence 2: this gradient estimator is biased from two sources: off-policy state sampling ρ β , and inaccuracies in the critic Q w . as we show in Section 4, we can bound the biases for all the cases, and in some cases, the algorithm still guarantees monotonic convergence as in Kakade & Langford (2002); Schulman et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Remarkably, Lever, Laviolette, and Shawe-Taylor are able to upper bound the KL divergence between the two distributions by a term independent of D, yielding the following result: Here kl(q||p) is the KL divergence between Bernoulli measures with mean q and p. See Section 4 for more details.
Sentence 2: assume 2 that, for every c > 0, there is a step size h > 0 and number of SGLD iterations n 2 O( 1 c q ), such that the n-th iterate w(S) 2 R p produced by SGLD satisfies W 2 P[w(S)|S], P[A (S)|S]  c. Markov's inequality and the definition of W 2 immediately implies the following.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We will use Xi as a shorthand for the collection of the ith coordinate of all the samples: The mean-squared loss of the protocol ⇧ with estimator ✓ is defined as and the communication cost of ⇧ is defined as The main goal of this paper is to study the tradeoff between R ⇣ (⇧, ✓), Proving Minimax Lower Bound: We follow the standard way to prove minimax lower bound.
Sentence 2: there has been a lot of work on the paradigm of studying communication complexity via the notion of information complexity [6,7,8,9,10].
Relationship: neutral
Domain: NeurIPS
Sentence 1: In practice, the DRIP and XCorr p-value computations are at least an order of magnitude slower than XCorr computation in Crux [21].
Sentence 2: in practice, scoring functions are often poorly calibrated (i.e., PSM scores from different spectra are difficult to compare to one another), leading to potentially identified spectra left on the table during statistical analysis.
Relationship: neutral