sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: The key idea is that, in the market from our first result, only about (log T ) 2 of the T participants can be informational traders; after this point, additional participants do not cost the designer any more budget, yet their transaction fees can raise significant funds.
Sentence 2: the market price update follows a natural kernel-weighted FTRL algorithm, where the learning rate λ is the price sensitivity of the market.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, both input neuroimaging measures (samples × features × time) and output cognitive scores (samples × scores × time) are 3D tensors.
Sentence 2: first, because LR and RR methods by nature can only deal with one individual cognitive measure at one single time point at a time, they cannot benefit from the correlations across different cognitive measures over the entire time course.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Overall, these results yield the insight that the shape of the entire distribution of a deep network's Jacobian singular values can have a dramatic effect on learning speed; only controlling the second moment, to avoid exponentially vanishing and exploding gradients, can leave significant performance advantages on the table.
Sentence 2: for hard tanh networks, p(q ⇤ ) = erf(1/ p 2q ⇤ ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, as we show in the experimental study (Section 5), popular probabilistic modeling systems such as JAGS [7] or Stan [8] reify the graphical model, resulting in unreasonable memory consumption for models such as LDA.
Sentence 2: indeed, it takes the collapsed LDA implementation 6.7 hours longer than Augur to draw 2048 samples.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Given state s and action a the next state s ′ is generated by s ′ = mod(s + 0.33a + 0.1randn, 1), where mod(x, 1) is the fraction part of x, and randn is a Gaussian random variable independent of the other variables in the problem.
Sentence 2: the distribution over the initial state is uniform.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When δ, ζ and µ −1 min are fixed, C 1 = O(p), which is intuitive as one needs to update p functions at a time.
Sentence 2: we set the discretization level δ = 0.05, the window size z = 3, the step size η k = (kδ/20 + 100) −1 , and the regularization coefficient ζ i,j ≡ ζ = 10 −8 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For ρ > 0 and 0 < α ≤ ∞ we say that h has geometric ρ-exponent α if Since {h > ρ} and {h ≤ ρ} are the classes which have to be discriminated when interpreting the DLD problem as a classification problem it is easy to check by Proposition 2.2 that h has geometric ρ-exponent α if and only if for P := Q s µ we have The latter is a sufficient condition for P to have geometric noise exponent α in the sense of [8].
Sentence 2: thus it is no surprise that R P (.)
Relationship: neutral
Domain: NeurIPS
Sentence 1: Experimental results demonstrate the comparative efficiency of our algorithms for sensor selection in high-dimensional distributions.
Sentence 2: full parallelization, wherein each node i ∈ V is viewed as separate computing resource, incurs a multiplicative overhead of O(diam(G)) due to each i having to send This overhead can be alleviated by instead assigning to every computational resource a connected subgraph of G. It should also be noted that if the quantification is instead performed using serial BP -which can be conceptualized as choosing an arbitrary root, collecting messages from the leaves up to the root, and disseminating messages back down again -a factor of 2 savings can be achieved for R 2 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: This has been one of the major criticisms of this type of encoding scheme as this result does not seem to be borne out experimentally (e.g., [19,2]).
Sentence 2: intuitively, expending more resources on accurately approximating the complete density of natural sensory statistics is inefficient (from an optimal control perspective) if the behaviorally relevant signals live in a compact subspace.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any Each observed variable x ∈ V obs is modeled as random vector in R d , and each hidden variable h ∈ V hid as a random vector in R k . The joint distribution over all the variables V T := V obs ∪ V hid is assumed satisfy conditional independence properties specified by the tree structure over the variables.
Sentence 2: in the discrete case, suppose that the observed variables take on d values, and hidden variables take k values.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With the above definitions, we show in the following theorem that when X and Y are both full row rank, (G 0 , E 0 ) is the unique solution to Eq.
Sentence 2: then models were obtained by applying each method to the remaining entries with a specific choice of λ from 10 −3 , 10 −2 , ..., 10 4 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We follow this particular approach since, first, CDFs can be easily estimated consistently using empirical CDFs without any free parameter, and second, standard tests on CDFs such as Kolmogorov-Smirnov (K-S) test [7] and Cramér-von-Mises (C-M) test [8] are well studied in the literature.
Sentence 2: other methods should be investigated that allow two spike trains to interact irrespective of their spike counts.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Next, since L i,t−1 is not assured anymore to be an upper bound on g t,i , we do not have any guarantee that the wealth Reward t,i is non-negative.
Sentence 2: we encode the gambler's bet in round t by a single number w t . The sign of w t encodes whether he is betting on heads or tails.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper, we considered a new class of bandit problems with unobserved confounders (MABUC) that are arguably more realistic than traditional formulations.
Sentence 2: the payout given by coin flipping is the same for both machines, P (Y = 1|do(X = M 1 )) = P (Y = 1|do(X = M 2 )) = 0.3, which means that the arms are statistically indistinguishable in the limit of large sample size.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any arms a = e|S ∈ A, we define the unit gap of a (i.e., the gap for one phase) as For any arms a = e|S ∈ A, we define the sunk-cost gap (irreversible once selected) as where for two feasible sets A and B, A ≺ B means that A is a prefix of B in some decision sequence, that is, there exists a decision sequence σ = S 0 = ∅, S 1 , . . , S k such that S k = B and for some j < k, S j = A.
Sentence 2: online combinatorial learning problem can be formulated as a repeated game between the environment and the player under stochastic multi-armed bandit framework.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let M n,P H (θ) = n −1 r nr m(a r , θ), where a r ∈ [0, 1] d is the center of B r , with a r (j) = (r j − 0.5)h n for all 1 ≤ j ≤ d. Comparing to θ * n,P H obtained by minimizing the exact integral, the only term in (8) impacted by using g(a r , θ) instead of h −d n Br g(x, θ)dx is the histogram bias term.
Sentence 2: . . , x n } ∈ X n , where X is the data universe.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let p k denote the value f (σ k ), for 1 ≤ k ≤ N . Without loss of generality we assume that the permutations are labeled such that p k ≤ p m for k < m. We write f (•) to denote the function and f to denote the vector (f (σ k )) N ×1 .
Sentence 2: consider a function f : S n → R. Suppose that f ℓ1 = 1 and we are given its corresponding Q.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the multinomial family £ ¦¥ ¨ § © E w0 , is an element of the 2 -simplex, ¥ ( gf ¢ B RQ ¢ B ¡ d . The transformation B 5 6 ih e B ¡ pG B maps the 2 -simplex to the 2 -sphere of radius 2.
Sentence 2: a "bag of words" representation was used for all three kernels, using only the word frequencies.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For this reason, we evaluate the score of each decoding, but show the most recent decoding rather than the best (as is standard in MAP) to simulate behavior in practice.
Sentence 2: , 31] give a class of easy-toevaluate upper bounds which can be directly optimized using coordinate descent [36,6], subgradient updates [14], or other methods [e.g.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A prior co-regularization based idea to harness unlabeled data in domain adaptation tasks demonstrated improved empirical results [10].
Sentence 2: we use an alternate formulation of the hypothesis classes and work in the original space X ⊂ R d . As discussed briefly in Section 2.2, EA can be thought to be simultaneously training two hypotheses h s = (g c + g s ) and h t = (g c + g t ) for source and target domains, respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this section, we present an iterative algorithm for computing both the conditional means and error covariances of a Gaussian process defined on any graph.
Sentence 2: if p(A) > 1, then the algorithm will not converge, whereas if p(A) < 1, then (xn -x) n~ 0 geometrically at rate 'Y ::@, p(A) 10.
Relationship: neutral
Domain: NeurIPS
Sentence 1: An orthogonal projection P i (φ(x j )) of a feature vector φ(x j ) into a subspace defined only by the set of indices i can be expressed as: P i (x j ) = X ( X X ) −1 Xφ(x j ), where X = X[i, :] are the i training examples from data matrix X.
Sentence 2: we give a novel bound that views the choice of subspace of the KMP algorithm as a compression scheme and hence provide a VC bound to upper bound its future loss.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In our experiment, the size of  In this section we mainly evaluate our proposed MetaAnchor on COCO object detection task [24].
Sentence 2: in addition, we introduce a data-dependent variant of anchor function generator, which takes the input feature x into the formulation: where r(•) is used to reduce the dimension of the feature x; we empirically find that for convolutional feature x, using global averaged pooling [13,38] operation for r(•) usually produces good results.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Two cornerstones of our ESS-CRF approach, namely using models that become more sparse when evidence is instantiated, and using multiple tractable models to avoid restrictions on the expressive power inherent to low-treewidth models, have been discussed in the existing literature.
Sentence 2: we have found it useful to regularize the conditional Chow-Liu (Alg.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If we instantiate the model as a CRF, the conditional probability of a truth assignment y to the hidden ground atoms (query atoms) in an MLN, given truth assignment x to the observable ground atoms (evidence atoms), is defined as: where f i,j (x, y) = 1 if the jth grounding of the ith formula is true under truth assignment {x, y}, and f i,j (x, y) = 0 otherwise.
Sentence 2: we will partition the weights (parameters) of our model based on whether they belong to transition or to emission part of the model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Since Q(v l ) is Gaussian, v l is always µ l at the optimal point and thus this optimization is equivalent to maximizing the determinant of the inverse covariance max Note that if T nl is one for all n, our method turns into a MAP-based sparse Gaussian process.
Sentence 2: our gating network is more flexible than previous generative approaches as inputs for each expert are modeled by a Gaussian mixture model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper we develop the SLEEC classifier to address both limitations.
Sentence 2: we now present our algorithm SLEEC which is designed primarily to scale efficiently for large L. Our algorithm is an embedding-style algorithm, i.e., during training we map the label vectors y i to L-dimensional vectors z i ∈ R L and learn a set of regressors V ∈ R L×d s.t.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Taking a closer look the following additional observations can be made: (1) During quantization the direction of vectors is better preserved with the forward pass compared to the backward pass; (2) validation accuracy follows tightly the cosine of the angle in the backward pass, indicating gradient quantization as the primary bottleneck; (3) as expected, the bound on E(cos(θ)) in Eq.
Sentence 2: for more complex models and challenging datasets, the extreme compression rate resulted in a loss of accuracy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This risk-sensitive Kalman filter is equivalent to a distributionally robust filter proposed in [12], which minimizes the worst-case mean square error across all joint state-output distributions in a Kullback-Leibler (KL) ball around a nominal distribution.
Sentence 2: the hope is that hedging against the worstcase distribution has a regularizing effect and will lead to a filter that performs well under the unknown true distribution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We concisely denote the transformation from a reference triangle to an observed triangle via a matrix A ∈ R 3×4 .
Sentence 2: mesh-ddcrp is significantly better than all other methods, including for settings of K which allocate 50% more parts to competing approaches, according to a Wilcoxon's signed rank test (5% significance level).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Stochastic search algorithms [1,2,3,4] are black box optimizers of an objective function that is either unknown or too complex to be modeled explicitly.
Sentence 2: due to the feature transformation, the output R [k] depends non-linearly on the projection W . Therefore, the posterior p(W |D) cannot be obtained in closed form any more.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We propose and study the known-compensation multi-armed bandit (KCMAB) problem, where a system controller offers a set of arms to many short-term players for T steps.
Sentence 2: update(↵ a2(t+1) , a2(t+1) , X(t + 1)) The third algorithm we propose is a Thompson Sampling (TS) based policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this example, the goal is to infer the rate θ of an exponential distribution, with a gamma prior p(θ) = Gamma(θ|α, β), based on M draws from Exp(θ): where r um = − ln(1 − u m ) (the inverse CDF of the exponential).
Sentence 2: the case D θ > D y is less interesting than the other ones above as we expect to have more summary statistics than parameters for most problems.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These included four UCI datasets 6 (ion, bupa, hepatitis and wine) and the previously used SRBCT data-set.
Sentence 2: formally, we look for a diagonal matrix F such that Σ ′′ i = Σ ′ i + F which also maintains x ⊤ Σ ′′ i x ≥ x ⊤ Σ i x for all x ∈ R d . we want to satisfy: where, for ease of notation, we take F(i) = F(i, i).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The heuristic that we chose for dimensionality reduction was simply one of reconstruction error, as in equation 5: a reduction that minimises reconstruction error should allow nearoptimal policies to be learned.
Sentence 2: pCA minimises squared error, while E-PCA with the Poisson loss minimises unnormalised KL-divergence, so it is no surprise that E-PCA performs better.
Relationship: neutral
Domain: NeurIPS
Sentence 1: At each step of iterative optimization, the method is guaranteed to reduce the discrepancy between the observed spectrogram and the spectrogram of the estimated waveform.
Sentence 2: let M = {m 1 , m 2 , m 3 ....} denote the spectrogram of s; m k is the magnitude spectrum of the kth window and m f k is the magnitude of the f th frequency component.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The variations of x as mostly restricted to an m 1dimensional subspace of R m , called the principal subspace, for some m 1 ≤ m. On this subspace we adopt a multivariate normal with mean µ ∈ R m1 and variance K ∈ R m1×m1 .
Sentence 2: from the observed values of x j ∈ R m , one can estimate the principal subspace and the covariance matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: By enforcing sparsity, we have thus increased the implicit limit on the number of bases that can be estimated without indeterminacy from the smaller dimension of V to the larger one.
Sentence 2: the aim of the model is to determine P (f |z) such that the model 1 PLSA actually represents the joint distribution of n and f as P (n, f ) = P (n) P z P (f |z)P (z|n).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Here we address an easier problem in which the analyst's queries only need to be answered when they overfit.
Sentence 2: let S be a random dataset in X n and A be an algorithm with range Y such that for some β ≥ 0, P[(S, We remark that mutual information between S and A(S) would not suffice for ensuring that bad events happen with tiny probability.
Relationship: neutral
Domain: NeurIPS
Sentence 1: 4 (d) and (e) correspond to the estimated temporal correlation β and the time average of µ, which is defined by µ n = 1 ∑ Tn t=1 µ n t , where T n denotes the sojourn time in the nth label or the total observation time T . The estimated temporal correlation differed significantly between the 1st and 2nd neural states (Wilcoxon signed rank test, p<0.00005).
Sentence 2: have proven the effectiveness of this method in estimating stationary firing rates [12].
Relationship: neutral
Domain: NeurIPS
Sentence 1: To achieve the CUR-type row sparsity, we propose the following modification of (4): Problem 2 (Group lasso SPCA: GL-SPCA).
Sentence 2: it computes a p × k orthogonal matrix W that minimizes Writing the SVD of X as UΣV T , the minimizer of ( 1) is given by V k , the first k columns of V. In the data analysis setting, each column of V provides a particular linear combination of the columns of X.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The analysis of FLL guarantees that the oblivious component of the player's expected regret (without counting the switching costs), as well as the expected number of switches, is upper bounded by O( √ T ), implying an expected regret of O( √ T ).
Sentence 2: we show that with switching costs, the attainable rate with bandit feedback is � Θ(T 2/3 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Mean-square and absolute-error regression: Our discussion assumes an even simpler form when the loss function D(., .)
Sentence 2: once again, this maximum likelihood problem may be regularized by prior information 1 , maximizing the a posteriori likelihood L(p) − q[p] instead of L(p); this problem is similarly tractable by ascent methods, by the concavity of −q[.]
Relationship: neutral
Domain: NeurIPS
Sentence 1: To test the robustness of this setting, we vary c over {0.1, 0.2, 0.5, 0.7, 1, 3, 5, 7, 9, 15, 30, 50} and keep v = = 0.1 ( and c play similar roles and so varying one is enough).
Sentence 2: we compare our DPMMGM with the well established KMeans, nCut and DPGMM clustering methods 3 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our approach builds on earlier work of Lawrence and Herbrich [2] which we extend here by considering randomized greedy selections and focusing on an alternative representation of the GP model which facilitates generalizations to settings such as regression and multi-class classification.
Sentence 2: when including i into the active set I, we need to update diag(A) and h accordingly, which in turn requires the matrices L and M to be kept up-to-date.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this work, we propose Covariance-Preserving Adversarial Augmentation Networks to overcome existing limits of low-shot learning.
Sentence 2: we propose Covariance-Preserving Adversarial Augmentation Networks (CP-AAN), a new class of Generative Adversarial Networks (GAN) [14,15] for feature augmentation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To see why this is useful, observe that minimising the pinball loss on scores F = f (X) is equivalently The second term on the right hand side is independent of ρ, and may be ignored.
Sentence 2: this will produce an estimate of the sublevel set where p(x) < ρ * (by Proposition 4), and ρ * corresponds to a quantile of f * (by Proposition 9).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Among the deep learning models, TrajGRU performs the best and 3D CNN outperforms 2D CNN, which shows that an appropriate network structure is crucial to achieving good performance.
Sentence 2: as rainfall events occur sparsely, we select the rainy days based on the rain barrel information to form our final dataset, which has 812 days for training, 50 days for validation and 131 days for testing.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In Section 3, we propose the parsimonious triangular model (PTM), in which the dimension of the triangle-generating parameters only grows linearly in K. The dramatic reduction is principally achieved by sharing parameters among certain groups of latent roles.
Sentence 2: nMI close to 1) across almost all networks, validating its ability to recover latent roles under a range of network sizes N and roles K. as N (and thus K) increases, MMSB Variational exhibits degraded performance despite having converged, while MMTM/PTM Gibbs converge to and become stuck in local minima  Mutual Information) and runtime per data pass for our method and baselines.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To complement this, we also propose a parameter-free algorithm, which still achieve a good regret bound and may have independent interest of its own.
Sentence 2: even when there is no variance in distributions, with Λ = 0, and the distributions only change once, with Γ = 2, any bandit algorithm cannot avoid a regret of about √ T , while a full-information algorithm can achieve a constant regret independent of T . Next, we study the tradeoff between Λ and V . We show that in the bandit setting, a regret of about 3 ΛV T + √ V T is achievable.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Once a stable matrix is obtained, it is possible to refine this solution.
Sentence 2: sVD yields D ≈ U ΣV T where U ∈ R m×n and V ∈ R τ ×n have orthonormal columns {u i } and {v i }, and Σ = diag{σ 1 , .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Finally we showed that our proposed method accelerated the learning phase when solving discrete and continuous domains using different learning algorithms.
Sentence 2: maintaining an estimate for each expert and state-action pair would not be practical for large spaces, so we follow Downey and Sanner [2010] and replace (σ i s,a ) 2 by the sample variance σ2 of D. This permits constant-time updates per sample without any additional memory overhead, and this worked very well in our experiments.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, the single treebank category NP (noun phrase) may be better modeled by several finer categories representing subject NPs, object NPs, and so on.
Sentence 2: many of the techniques used in [12,14] are orthogonal to what was presented here (additional non-local/overlapping features, merging of unnecessary splits) and could be incorporated into the discriminative model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We denote the subset of views that specify the effects for action a by T a ⊂ T . The main challenge is to build and maintain a comprehensive set of views that can be used in new environments likely resembling the old ones, but at the same time allow adaptation to new tasks with completely new transition dynamics and feature distributions.
Sentence 2: unlike our work, these studies usually assume a common concrete state space.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any fixed , letting N = 0 , it follows that ).
Sentence 2: observe that the term tr(D 0 Ñ † D K) is again jointly convex in Ñ and D (also a perspective function), while it is easy to verify that L1 (D K, Ñ ) as defined in Lemma 3 below is also jointly convex in Ñ and D [32]; therefore the objective in ( 8) is jointly convex.
Relationship: neutral