sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: For these experiments, we initialize both the methods with an initial labeled dataset of 100 points and then after each active learning round we seek all the labels for the selected training data point.
Sentence 2: first, consider the simpler scenario where the training data set only consists of fully labeled instances X L with labels Y L . Thus our aim is to infer p(Y U |X, Y L , Φ), the posterior distribution over unlabeled data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the following, we refer to Φ, defined by parameters (α, p), as the true stochastic model under which all the observed random labels are generated, and denote by ) the corresponding probability measure (resp.
Sentence 2: we can relate I to D(α, p): Claim 5 In the LSBM with K clusters, if p = o(1), and for all i, j, such that i = j, α i = 1 K , p(i, i, ) = p( ), and p(j, k, ) = q( ), we have: Again from this claim, the results derived in [13] are obtained by applying Theorem 3 and Claim 5.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Their use of an auxiliary sample set and the notion of average distance between partitions makes their bounds conceptually different from our work.
Sentence 2: we have the following upper bounds on gen(µ, P W |S ) and gen + (µ, P W |S ) based on the mutual information between the training set S and the discretized output of the learning algorithm, where each of these mutual information terms is multiplied by an exponentially decreasing weight 2 −k , in which the exponent measures how finely the output W of the learning algorithm is discretized: Theorem 3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For example, Wilson and Nickisch [27] proposes to space the inducing points on a multidimensional lattice, so the time and space complexities of using a product kernel becomes O(N + DM 1+1/D ) and O(N + DM 1+2/D ), respectively.
Sentence 2: algorithm 1 summarizes the online learning procedure used by all stochastic algorithms, 12 where each learner has to optimize all the parameters on-the-fly using i.i.d.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is often claimed that small saccades are necessary to refresh neuronal responses and prevent the disappearance of a stationary scene, a claim that has remained controversial given the brief durations of natural visual fixation (reviewed in [16]).
Sentence 2: it is difficult, however, to envision how such steady-states could occur under natural viewing conditions, given that the projection of the visual scene on the retina is never stationary.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This material is based upon work supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF-1231216, and the Italian Institute of Technology.
Sentence 2: it is clear from definition (1) that an exact leverage scores computation would require the same order of computations as an eigendecomposition, hence approximations are needed.The accuracy of approximate leverage scores is typically measured by t > 0 in multiplicative bounds of the form Before proposing a new improved solution, we briefly discuss relevant previous works.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unfortunately, none of these approaches strictly enforce prior logical relationships between label predictions.
Sentence 2: for example, s might decompose as s(x, y) = c∈C s(x, y c ) over a set of cliques C that form a junction tree, where y c denotes the portion of y covered by clique c. Y might also encode constraints to aid tractability, such as y forming a consistent matching in a bipartite graph, or a consistent parse tree [28].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Thus a first-order HMM for an alignment between e ≡ e 1:I and f ≡ f 1:J is defined as: where p(a j |a j−1 ) is the state transition probability; J and I are sentence lengths of the French and English sentences, respectively.
Sentence 2: the English topics (represented by the topic-specific word frequencies) can be directly read-off from HM-BiTAM parameters β.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the unnormalized model (2) and distributions p(x) and p(x) in P , probability functions r α,θ (x) and rα,θ (x) on X are defined by The distribution r α,θ (r α,θ ) is an e-mixture model of the unnormalized model (2) and p(x) (p(x)) with ratio α [11].
Sentence 2: the estimating equation of the MLE is written as which is a moment matching with respect to the empirical distribution p = r1,θ mle and the normalized model qθ = r0,θ mle .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The best model fit from 200 random restarts (lower bound of −2.24 × 10 4 , no crossvalidation, results not shown) only used 3 out of the 8 possible states (the other 5 states had a probability of less than 0.5 %).
Sentence 2: the model allows state-transitions to be dependent on an external input x t -this can e.g.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the remainder of the text, we consider θ to be an [n(n + 3)/2]-dimensional column vector consisting of the elements of w and the upper-right elements of C, i.e., Here, C k:n,k is the sub-matrix in C at row k to n and column k. Previous natural policy gradient methods [9] use the empirical FIM, which is estimated from a sample path.
Sentence 2: in this approach, the action of the agent is the parameters of the controller, and the policy is represented by where Σ is the n × n covariance matrix and the agent seeks θ = w, Σ .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In practice, neither the form of C nor the form of Σ is known a priori and hence needs to be inferred from data, fitting a set of corresponding covariance parameters θ C and θ Σ .
Sentence 2: in the following, we will refer to a Gaussian process model with this type of sum of Kronecker products covariance structure as GP-kronsum 1 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In our setup, the output of the neuron during learning is clamped to the teacher spike train S * which is the output of a neuron with the target weight vector w * .
Sentence 2: on the other hand experiments in vivo have shown that neurons can be taught by suitable teacher input to adopt a given firing response [2,3] (although the spiketiming dependence is not exploited there).
Relationship: neutral
Domain: NeurIPS
Sentence 1: d P fe ¡ g &g ' where $ & @' s% ¤!
Sentence 2: moreover, at the fixed points, x W `Y Fa 8 a vu ti H . Corollary 5.5 When § ¤¢ every algorithm which finds a fixed point of 8 , induces a fixed point of u with ¥¢ , and vice versa.
Relationship: neutral
Domain: NeurIPS
Sentence 1: According to our notation, for every i, Theorem 2.1 Assume 0 < E(h 2 ) < ∞, then under H A , ηk converges in distribution to a Gaussian according to where This in turn implies that For an average of {η k (i)} i=1,..., n B , the central limit theorem implies that under This result shows that the distribution of H A is asymptotically independent of the block size, B.
Sentence 2: this effect will vanish as n grows.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As the drift v was fixed in CONST, this variant explained coherence-dependent behaviour with large and almost identical changes in both diffusion s and bound b such that large parameter values occurred for small coherences and the relation between parameters and coherence appeared to be quadratic.
Sentence 2: the brain, therefore, must had adapted reliability within trials even on the short timescale of a few hundred milliseconds.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this case, each feature vector Xn at time n is considered as a fixed length sequence, which has supposedly been generated by a temporal HMM state specific HMM for which each state is emitting individual feature components that are modeled by, e.g., one dimensional Gaussian mixtures.
Sentence 2: ------------------- , ___________________________________________________ _ Figure 1: Typical multiband-based ASR architecture.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let f ∈ R V and denote by C t := {i ∈ V | f i > t}, then it holds under both conditions, Theorem 3.1 can be generalized by replacing the cut with an arbitrary other set function.
Sentence 2: if F : A → g(s(A)) is submodular for all s ∈ R V + , then g is concave.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Because the color likelihood p C (y | x i , z i ) factorizes across pixels u, the BP approximation to p C (y | x i ) may be written in terms of these marginal occlusion probabilites: Intuitively, this equation downweights the color evidence at pixel u as the probability of that pixel's occlusion increases.
Sentence 2: this research was supported in part by DARPA Contract No.
Relationship: neutral
Domain: NeurIPS
Sentence 1: . . , i k , together with the rows e i1 , .
Sentence 2: bob, who has [1, 0 d ] together with the output P , can compute the second row of AP , which necessarily reveals a lot of information about x (e.g., if AP ≈ [1, x/2; 1, x/2], its second row would reveal a lot of information about x), and therefore one could hope to embed an instance of the Index problem into x.
Relationship: neutral
Domain: NeurIPS
Sentence 1: T y M maps a vector v 2 T x M to y x v 2 T y M, while preserving norm, and roughly speaking, "direction," analogous to translation in R d . A tangent vector of a geodesic remains tangent if parallel transported along .
Sentence 2: for the problem of computing the leading eigenvector, i.e., min existing analyses for state-of-the-art algorithms typically result in O(1/ 2 ) dependence on the eigengap of A, as opposed to the conjectured O(1/ ) dependence [29], as well as the O(1/ ) dependence of power iteration.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let {P k } ∞ k=k1(T ) be an increasing sequence of partitions of T , where for each Note that in Theorem 4 if we let T W and X w gen(w) for all w ∈ W, then for each k ≥ k 1 (T ), due to the Markov chain and the data processing inequality, we have I([W ] k ; X T ) ≤ I([W ] k ; S).
Sentence 2: the fact is that we are not dealing with infinite number of independent random variables: the random variables h t (G 2 ) and h s (G 2 ) are actually quite dependent on each other when t and s are close.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In general, the TD model has learned that the radar screen and direction finder (toward the bottom left of the game screens) are usually the relevant locations, as illustrated by the elevated activity at those locations in the sample TD maps in row g. Most of the time, that is indeed a good prediction of eye position, reflected by the fact that the TD NSS scores are typically higher than the BU NSS scores outside the event window.
Sentence 2: we annotated the video game clips with several pieces of additional information that we could use to identify interesting events (see Figure 2) which would serve as the basis for event-locked analyses.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Thus all the information in the population spike train can be summarized in the random vector ∆(r), which is a simple linear function of the observed spike train data.
Sentence 2: in this paper, we study information transmission and optimal decoding in what we would argue is a more biologically-relevant "intermediate" regime, where n is large but the total amount of information provided by the population remains finite, and the problem of decoding the stimulus given the population neural activity remains nontrivial.
Relationship: neutral
Domain: NeurIPS
Sentence 1: With this notation Y = AX −1 + G . We can apply Corollary 1.1 directly once we have suitable bounds on G and U G . The result of [MCJ13] is specific to the spiked covariance model.
Sentence 2: this step loses control of the coherence of the original matrix and hence results in suboptimal bounds.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A useful property motivating the use of GPs is that linear projection preserves normality, so that the posterior distribution for the integral p[f ] is also a Gaussian, characterised by its mean and covariance.
Sentence 2: require: function J, initial state g 1 = ḡ1 ∈ G (and, for FW only: step-size sequence {ρ i } n i=1 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: When t = 1, our proposed EP for the t-exponential family is reduced to the original EP for the ordinary exponential family and t-factorization yields the ordinary data-dependent factorization.
Sentence 2: as shown in the previous section, ADF has been extended to EP (which resulted in moment matching for the exponential family) and to the t-exponential family (which yielded escort moment matching for the t-exponential family).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Here (2 is useful to single out the triple wise interaction (()3 = 8123 ), while (I is to single out the pairwise and triplewise interactions together (()2; ()3).
Sentence 2: for example, when we compare firing patterns in two periods, as control and 'test' periods, there may exist a weak correlation in the control period.
Relationship: neutral
Domain: NeurIPS
Sentence 1: One of the simplest processes that can operate over a semantic network is a random walk, stochastically jumping from one node to another by following edges.
Sentence 2: in our analyses we consider only the first time an animal node is visited, which we denote as τ (k) for the k th unique animal seen on the random walk (out of the K unique animals seen on the random walk).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Input: Empirical second-moment matrices Σ x,y for all pairs {x, y} ⊂ V obs computed from N iid samples from the distribution over V obs ; threshold parameters ∆ x,y for all pairs {x, y} ⊂ V obs .
Sentence 2: suppose the Spectral Recursive Part of this work was completed while DH was at the Wharton School of the University of Pennsylvania and at Rutgers University.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Third, for the same reason (because R P (P, X) depends directly on P rather than particular data X 1:n ), it detect lack-of-diversity issues such as mode collapse.
Sentence 2: to ensure that the summation is well-defined, the order of summation will need to be specified, depending on the application (as in, e.g., Section 6).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that although the predicted configurations are not the true MAP labelings, they correctly match the training labels.
Sentence 2: for positive constants λ ij , define edge potentials ψ ij (y i , y j ) = exp(λ ij ) whenever y i = y j and ψ ij (y i , y j ) = 1 otherwise.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In future work, we will determine the number of topics automatically by extending the proposed model to a nonparametric Bayesian model such as the Dirichlet process mixture model [24].
Sentence 2: each annotation is associated with a latent variable r dm with value r dm = 0 if annotation t dm is not related to the content; r dm = 1 otherwise.
Relationship: neutral
Domain: NeurIPS
Sentence 1: #@ ) C ED GF 1 98 ¡ %$ & R C GD EF 1 98 ¡ %$ P " D 8 ¡ %$ P ' , PF enables us to compute i particles ¡ ) C GD EF 1 98 ¡ R C GD EF 1 98 ¡ ¢ H D EP approximately distributed according to !
Sentence 2: this discrepancy is what causes the well known problem of sample impoverishment in all particle filters [11,15].
Relationship: neutral
Domain: NeurIPS
Sentence 1: This will almost inevitably lead to overfitting (in a maximum likelihood context) or inflated inference uncertainty (in a Bayesian context).
Sentence 2: the conjugate prior for the hyperparameters a, b is a beta distribution, P (a, b|α, α, γ, γ) ∝ a 1) , which allows the hyperparameters to be integrated out in closed form: .
Relationship: neutral
Domain: NeurIPS
Sentence 1: One of the disadvantages of this approach, from an image coding perspective, is that it may only be applied to small sub-images (e.g., 12 x 12 pixels) extracted from a larger image.
Sentence 2: moreover, the resulting coefficients achieve higher coding efficiency (higher SNR for a fixed bit-rate) than traditional wavelet bases which are typically designed "by hand" according to certain mathematical desiderata [5].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Both models have a power-law distribution with an exponent approximately equal to -3/2, although the exponent is somewhat smaller for small network sizes.
Sentence 2: we consider time being measured in discrete steps, t = 0, 1, 2, . . .. Because synaptic values are essentially determined presynaptically, we assume that all synapses of a neuron are identical, i.e.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper, we assume that each w i has a multivariate Gaussian N (0, σ 2 I n×n ) distribution.
Sentence 2: b 3 (ξ, ρ n , n, s) (ii) If the support minimum B min > 2b 3 (ξ, ρ n , n, s), then the primal support method successfully recovers the support union J = S(β 1 )∪S(β 2 ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is formalized as follows: we are given a compact convex set K that contains a global minimum of f , i.e., ∃z ∈ K such that z ∈ arg min x∈R d f (x).
Sentence 2: this project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no 725594 -time-data).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We show that a Bayes-risk minimizing decision policy that minimizes not only error rate but also average decision delay naturally exhibits the experimentally observed Go bias.
Sentence 2: experimental evidence also indicates that there is a curious choice bias toward the overt (Go) response in the GNG task [11,16,2,15], in the form of shorter response times and more false alarms for the Go response, than when compared to the same stimulus pairings in a 2AFC task [2,16].
Relationship: neutral
Domain: NeurIPS
Sentence 1: As a first step towards end-to-end learning, hand-crafted descriptors like SIFT [9,10] or detectors [9,11,12] have been replace with learned ones, e.g., LIFT [13], MatchNet [14] and DeepCompare [15].
Sentence 2: in this paper, we focus on descriptor learning and, using a novel method, train a convolutional neural network (CNN), called HardNet.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In brief, the sampling distribution f 1 (j) and the model dependency control scheme with threshold ρ allow STRADS to speed up the convergence rate of Lasso.
Sentence 2: because our experiments feature very large vocabulary sizes, even a small fraction of the word-topic table can still be too large for a single machine's memory, which caused YahooLDA to fail on the larger experiments.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The data center then collects the L codeword sequences, z 1 , • • • , z L . Since all the L codewords are of the same length m, the combined data rate will be R = L × m/n.
Sentence 2: in this paper, we introduce a new analytical model for a massive sensing system with a finite data rate R. More specifically, we assume that the sensors use LDGM codes for rate distortion coding, while the data center recovers the original sequence by using optimal "majority vote" estimation [3].
Relationship: neutral
Domain: NeurIPS
Sentence 1: We apply this RL based interactive retrieval framework to the task of image retrieval, which we call dialog-based interactive image retrieval to emphasize its capability in aggregating history information compared to existing single turn approaches [13,14,15,16].
Sentence 2: for example, if the "shiny" value of the candidate image and the target image are 0.9 and 1.0 respectively, then the rule-based feedback is "more shiny."
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that a D input lattice interpolated with simplex interpolation has D!
Sentence 2: in this paper, we proposed combining three types of layers, (1) calibrators, (2) linear embeddings, and (3) multidimensional lattices, to produce a new class of models we call deep lattice networks that combines the flexibility of deep networks with the regularization, interpretability and debuggability advantages that come with being able to impose monotonicity constraints on some inputs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The second bound is much more useful (and, as we show below, tight) in the data-sparse regime N << m. The resulting minimization problems have a polynomial approximation flavor: we are trying to find an optimal set of weights g j such that the sum in the definition of f (t) (a polynomial in t) will be as close to H(t) + t as possible.
Sentence 2: the first is nearly tight for N >> m (it is actually asymptotically possible to replace m with m − 1 in this limit, due to the fact that p i must sum to one; see (7,8)), but grows linearly with m and thus cannot be tight for m comparable to or larger than N . the optimizer doesn't depend on m, only N (and hence the bound can't help but behave linearly in m).
Relationship: neutral
Domain: NeurIPS
Sentence 1: We now have the notation to consider a popular class of M -estimators studied in the papers above for these superposition-structured models: where {λ r } k r=1 are regularization penalties.
Sentence 2: . . , d (k) ] = argmin The quadratic subproblem (8) cannot be directly separated into k parts because the Hessian matrix ( 7) is not a block-diagonal matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: where I w (t 1 i , t 2 j ) is a function that returns 1 iff t 1 i = w and t 2 j = w, and 0 otherwise.
Sentence 2: the sequence and tree kernel with feature selection (SK,TK+FS) can be defined as follows: (2) The difference with their original kernels is simply the condition of the first summation, which is τ ≤ χ 2 (u).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The deformation features φ stich d (p i , s, θ) between the face p i and the stitching point s are defined as Here, (u(s, i), v(s, i)) is the position of the stitching point in the rectified coordinates corresponding to face i and level l. We define the deformation cost between the faces to be a function of their relative dimensions: with e i and e k the lengths of the common edge between faces i and k. We define the deformation of a face with respect to the stitching point to also be quadratic.
Sentence 2: object-centered approaches represent and reason about objects using more sophisticated 3D models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We select the training input density Ô Ü ´Üµ from the independent Gaussian density with mean Å Ä and standard deviation Å Ä , where In this simulation, we can not create the training input points in an arbitrary location because we only have ½ ¾ samples.
Sentence 2: for each run, the test errors of (A) and (B) are normalized by the test error of (C), and then the values are averaged over ½¼¼ runs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The key result is that, when testing between two multivariate Poisson distributions of means log(n)λ 1 and log(n)λ 2 respectively, where λ 1 , λ 2 ∈ Z k + , the probability of error (of maximum a posteriori decoding) is n −D+(λ1,λ2)+o (1) .
Sentence 2: proving that the number of non-backtracking walks is close to its expected value is difficult.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this section, we discuss how the PixelGAN autoencoder can be viewed in the context of learning cross-domain relations between two different domains.
Sentence 2: the adversarial training pushes the output of the encoder to the corners of the softmax simplex, by which it ensures that the autoencoder cannot use the latent vector z to carry any continuous style information.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The problem of learning a (k, `)-binary-biclustered matrix, corresponds to the assumption that the row indices and column indices represent k and `distinct object types and that there exists a binary relation on these objects which determines the matrix entry.
Sentence 2: the number of margin violations in a sequence S at complexity is defined to be, merr(S, ) := inf note that merr(S, ) = 0 if  1 mc(S) .
Relationship: neutral