sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: We propose a new search paradigm of active information retrieval in which the user initiates only one query, and the subsequent iterative process is led by the engine/system.
Sentence 2: with these changes, we obtain: (2) bs J(Y i 8. ll) = -+ log(as) -w(as + 1) We can optimize the choice of S with a simple greedy method that successively finds the next best cluster index i to include in the information set.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the following section, we will investigate how to find the optimal tradeoff between sparsity and variance for the sparsification technique.
Sentence 2: the whole protocol can be summarized as follows: where We note that if g is an unbiased estimate of the gradient, then Q(g) is also an unbiased estimate of the gradient since In distributed machine learning, each worker calculates gradient g and transmits it to the master node or the parameter server for an update.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As we have already shown in Figure 1, the reaching period data are strongly under-dispersed, even absent conditioning on the latent dynamics (implying further under-dispersion in the observation noise).
Sentence 2: with θ controlling the (log) rate of the distribution and g(•) controlling the "shape" of the distribution, the GC family provides a rich model class for capturing the spiking statistics of neural data.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A significant difference between our previous work [9] and this paper is that scalability is achieved in our earlier work by restricting the approach to "egocentric" modeling, in which counting processes are placed only on nodes.
Sentence 2: in this case, estimating time-varying coefficients improves predictive performance, which makes sense because we have seen in Figure 3 that METAFILTER's coefficients tend to vary more over time.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To organize goal-oriented behavior we assume that, in parallel to the activation dynamics (1), there exists a second dynamic process which can be motivated from classical approaches to Reinforcement Learning [11,12].
Sentence 2: we chose a modulation of the following kind: To every existing connection (ji) we associate a codebook vector a ji onto the motor layer which is compared to the current motor activity a via a Gaussian kernel function k a .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We see, first, that CMICOT with t ≥ |F int | significantly outperforms all baselines, except the idealistic CMI method whose results are similar to CMICOT.
Sentence 2: we refer to this FS method as CMICOT (Conditional Mutual Information with Complementary and Opposing Teams) and present its pseudo-code in Algorithm 1, which has a form of a SFS strategy with a specific algorithm to calculate the score (lines [10][11][12][13][14][15][16][17][18][19].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Intuitively speaking, such q init already encodes certain preferences towards a few preconditioned shift truncations of the ground truth.
Sentence 2: 6 In light of the above observations, a natural computational approach to sparse blind deconvolution is to attempt to find x 0 by searching for a sparse vector in the linear subspace row(X 0 ), e.g., by solving an optimization problem where • is chosen to encourage sparsity of the target signal [20,21,22,23].
Relationship: neutral
Domain: NeurIPS
Sentence 1: regret) to scenarios where learner is constrained to a unit ball of an arbitrary Banach space (not necessarily and p space) and the objective functions have sub-gradients that lie in the dual ball of the space-for reasons that will become clear shortly, we refer to this as the data domain.
Sentence 2: on the other hand given a matrix W , its max-norm is given by .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our computing network consists of m machines, where machine i stores X i , y i = (S i X, S i y) and S = S 1 S 2 . . . S m . The optimization process is oblivious to the encoding, i.e., once the data is stored at the nodes, the optimization algorithm proceeds exactly as if the nodes contained uncoded, raw data (X, y).
Sentence 2: using the existing results on the eigenvalue scaling of large i.i.d.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that in the term tr(WΣ −1 W ⊤ ), the inverse covariance matrix Σ −1 plays the role of coupling pairs of weight vectors, and therefore controls the amount of sharing between any pair of tasks.
Sentence 2: among other works, Graph-guided Fused Lasso [11] (GFlasso) incorporates task structure to some degree by assuming that the regression coefficients of all the outputs have similar sparsity patterns.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The lengthscales are set to 14.5 m and the prior standard deviation of heights is 10 m. We assume a noise standard deviation of 0.075 m. Since the safety feature of each state transition is a linear combination of heights, the GP model of the heights induces a GP model over the differences of heights, which we use to classify whether state transitions fulfill the safety constraint.
Sentence 2: we introduce SAFEMDP, a novel algorithm for safe exploration in MDPs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We illustrate the concept on simulated data: We will use a similarity measure based on the metric D interval [ 1 9] to estimate the receptive field of a neuron which does not use its firing rate, but rather the occurrence of specific interspike intervals to convey information about the stimulus.
Sentence 2: right from the first synapse, the information of an individual photoreceptor is signaled to many different cells with different temporal filtering properties, each of which is only a small unit within a complex neural network [ 20] .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each game, subjects first practiced the game for several one-hour sessions on different days until reaching a success criterion (definition follows), and then returned for a one-hour eye tracking session with that game.
Sentence 2: these windows then propagate through our model-based analysis, where we compare the eye position traces (row c) with the maps predicted by the BU salience (row f) and TD relevance (row g) to generate a continuous sequence of NSS values for each model (row d).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the linear case, MSPBE was chosen as a projection of the Bellman error on a natural hyperplane-the subspace to which V θ is restricted.
Sentence 2: to illustrate the convergence properties of the algorithms, we applied them to the "spiral" counterexample of Tsitsikilis & Van Roy (1997), originally used to show the divergence of TD(0) with nonlinear function approximation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A policy π is some decision tree that represents a strategy for adaptively selecting items.
Sentence 2: there have been several studies on adaptive submodular maximization in other settings, for example, selecting multiple instances at the same time before observing their states [7], guessing an unknown prior distribution in the bandit setting [18], and maximizing non-monotone adaptive submodular functions [22].
Relationship: neutral
Domain: NeurIPS
Sentence 1: From the above, for n sufficiently large, the maximizer of the KDE in [y 0 − 2τ, y 0 + 2τ ] ∩ Y is contained in [y 0 − τ, y 0 + τ ].
Sentence 2: if x 1 and x 2 are (r s , δ)-separated, then there cannot exist a directed path from x 1 to x 2 in G. Proof.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Efficient trades are unique up to zero-sum cash transfers: Given efficient trades dr * , dr ∈ R N on S, we have dr = dr * + (z 1 r $ , .
Sentence 2: we say F is L i -Π i -smooth if for all i there are constants L i > 0 such that for all y ∈ im(Π i ), Finally, let F min := min y∈span{im(Πi)}i F (x 0 + y) be the global minimizer of F subject to the constraints from the Π i .
Relationship: neutral
Domain: NeurIPS
Sentence 1: As with the Bethe approximation and its generalizations [12], the optimizing arguments of this problem can be taken as approximations to the exact marginals.
Sentence 2: (for a graph G = (V, E), we simply set θ st = 0 for all pairs (s, t) / ∈ E.) We first focus on the marginal polytope MARG(K n ) ≡ MARG(K n ; φ) of valid dual variables {µ s , µ st }, as defined in Eqn.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Regretfully, this goal turns out to be impossible without making additional assumptions.
Sentence 2: . . , (x T , y T ) be a sequence of examples such that K(x t , x t ) ≤ 1 for all t. Let g be an arbitrary function in H K and define lt = ℓ g; (x t , y t ) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We propose a novel method with provable guarantees for unsupervised estimation of discrete graphical model mixtures.
Sentence 2: note that for a general graph G ∪ with treewidth tw(G ∪ ) and maximum degree ∆(G ∪ ), we have that η ≤ min(∆(G ∪ ), tw(G ∪ )).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that Lévy flights (i.e., randomly selecting a flight direction and then execute a flight distance that has power-law scaling as in Equation 1) are random walks and so produce 1/f 2 noise instead of 1/f noise (see Supplementary Material for details).
Sentence 2: additionally, it may be that a cognitive load manipulation would reduce the number of available chains and thus reduce exploration, which is an interesting prediction to test in future work.
Relationship: neutral
Domain: NeurIPS
Sentence 1: These terms are a consequence of the special case analysis for L 1 norm.
Sentence 2: (10) The right hand side of the inequality has two issues: it depends on θ * , and it is a random variable, since it depends on Z n . In this section, we characterize E[R * (∇L(θ * ; Z n ))] in terms of the Gaussian width of the unit norm ball Ω R = {u : R(u) ≤ 1}, and also discuss large deviation bounds around the expectation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We define the following key geometric constant that capture the impact of manifold curvature: We note that most (if not all) practical manifold optimization problems can satisfy these assumptions.
Sentence 2: with assumptions and parameters in Theorem 2, choosing ↵ 1 = 2/3, the IFO complexity for achieving an ✏-accurate solution is:  The same reasoning allows us to also capture the class of gradient dominated functions (2), for which Reddi et al.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Multi-dimensional scaling can be used for this purpose.
Sentence 2: if we denote T X = [log µ (x i )], the matrix of tangent vectors corresponding to all data-points, and if Π is the permutation matrix that orders the columns such that the first K columns of T X correspond to the most diverse selection, then Here, R 11 ∈ R K×K is the upper triangular matrix of R ∈ R n×n , R 12 ∈ R K×(n−K) and R 22 ∈ R (n−K)×(n−K) .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Tuning is a major problem for these methods, since it requires rough knowledge of the optimal value.
Sentence 2: we may employ Jensen's inequality to bound its error as follow, Combining this with T −1 t=0 α t ≥ Ω(T 2 ), implies that in order to substantiate the proof it is sufficient to show that, , is bounded by a constant.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The solution ŵ can therefore be interpreted as the superposition of a vector which has small `2 norm, and a vector which has small k-support norm, with the parameter a regulating these two components.
Sentence 2: a classical result by von Neumann [10] establishes that a norm is orthogonally invariant if and only if it is of the form kW k = g( (W )), where (W ) is the vector formed by the singular values of W in nonincreasing order, and g is a symmetric gauge function, that is a norm which is invariant under permutations and sign changes of the vector components.
Relationship: neutral
Domain: NeurIPS
Sentence 1: So using much larger depths may lead to bad performance (On Movie, tree depth h = 18: K-L = 0.1162 vs h = 9: K-L = 0.0831).
Sentence 2: x, i.e., the mapping function g, is defined by g(x; Θ, T ) = ∈L p( |x; Θ)q .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We perform the Gaussian kernel experiment similarly with model parameter C equals to 2 i , i = {0, 3, 6, 9, 12} and kernel parameter γ equals to 2 i , i = {−12, −9, −6, −3, 0} in the first stage.
Sentence 2: we then show that adding other rows and columns in L xi,w to the game matrix does not change the game value.
Relationship: neutral
Domain: NeurIPS
Sentence 1: At each iteration, the computational cost is dominated by the update of Z (−n) (n = n), which can be obtained by where (−n, −n) denotes every mode except n and n, which greatly reduces the computation.
Sentence 2: note that when α > 0, each subproblem is strongly convex and the generated solution sequence is uniformly bounded, we can show that ACS can converge to a coordinate-wise minimum point of (8) with properly chosen initial value [Mishra et al., 2017].
Relationship: neutral
Domain: NeurIPS
Sentence 1: [5] proposed a similar problem, namely robust principal component analysis (RPCA), which studies the problem of recovering the low-rank and sparse matrices by solving a convex program.
Sentence 2: in order to address this problem, [15] [20] extended the trace norm of matrices [19] to tensors, and generalized convex matrix completion [8] [7] and matrix decomposition [6] to convex tensor completion/decomposition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: ( 23) since placing a Dirac delta outside a convolution will result on a degenerate covariance.
Sentence 2: we will calculate the statistics of the complex-valued F c (ξ) for notational simplicity, to then calculate the statistics of the real-valued processes F c (ξ) and F c (ξ) according to: The above expressions are due to the identity in eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The norm is defined, for every W 2 R d⇥m , as where S m = {S 2 R m⇥m , S ⌫ 0 : aI S bI, tr S = c}, and 0 < a  b.
Sentence 2: as a tends to zero, in order to prevent the objective from blowing up, û must also tend to zero and we recover k-support norm regularization.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our approach is learn one density model for the benign feature vectors and a second density model for the malignant feature vectors and then use Bayes rule to classify an input vector.
Sentence 2: the hidden variables are independent and normally distributed with zero mean and unit variance: ( The input is modeled as a linear combination of the hidden variables, plus independent Gaussian noise: (2) The model parameters are the factor loading matrix A and the diagonal matrix of sensor noise variances, \]f. Factor analysis (d. (Rubin and Thayer 1982)) is the procedure for estimating A and lJI using a training set.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This likelihood can be obtained analytically since after linearization of (4) with respect to µ l n (t) at µ l(i) n (t − 1), an extended Kalman filter (EKF) can be obtained, where the prediction likelihood of the EKF gives the weight, and the updated continuous state of EKF gives µ l(i) n (t).
Sentence 2: it is well-known that noise statistics may vary during recognition.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The BCM can yield high-quality predictions that avoid the pitfalls of local GPs (Figure 1c), while maintaining scalability to very large datasets [12].
Sentence 2: if the noise is iid Gaussian, i.e., ε ∼ N (0, σ 2 n I), then the observations are themselves Gaussian, y ∼ N (0, K y ), where K y = k θ (X, X) + σ 2 n I.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Conceptually, the log-likelihood objective implicitly trades off between model error in different regions of the input/output space, but does so in a manner largely opaque to the modeler, and may ultimately not employ the correct tradeoffs for a given task.
Sentence 2: (x; ✓), yet we adapt this model based on the task loss instead of any model prediction accuracy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: expression quantitative trait loci (eQTL) mapping in computational biology [28], land surface temperature prediction in climate informatics [17], neural semantic basis discovery in cognitive science [30], etc.
Sentence 2: in fact, this seemingly restrictive setting is general enough to encompass the model with response-specific parameters, which can be realized by block-diagonalizing rows of X i and stacking all coefficient vectors into a "long" vector.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For any ✏ 2 (0, 1], it holds that Our assumptions on the loss functions, as the Lipschitz assumption or the smoothness assumption, are stated in terms of the standard Euclidean norm (which we denote by k • k 2 ).
Sentence 2: . . , ĝT that can plug into the dual averaging algorithm.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We thus have and where in the last line, we use the Taylor expansion again to expand f around Q k c + 1 − Q 2 k e and the bracket • denotes the average over two independent random variables c ∼ P c and e ∼ N (0, 1).
Sentence 2: to simplify the PDE in (6), we can assume that the two functions Q t and R t in ( 7) and ( 8) are given to us in an oracle way.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Both of them are outperformed by PBM-TS and PBM-PIE.
Sentence 2: to get the expression given in Theorem 6 from Corollary 5, we proceed as in [6] showing that the optimal coefficients (c a ) a∈A can be non-zero only for the K − L actions that put the suboptimal arm k in the position l that reaches the minimum of ∆ v k,l (θ)/d(κ l θ k , κ l θ L ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: The second says that reflecting twice gives back the original string, and the third says that left-shifting then reflecting is the same as reflecting and then right-shifting.
Sentence 2: we recall that the kernel of a group homomorphism π : G → G is a normal subgroup of G, and that normal subgroups N of G are invariant under the operation of conjugation by elements g of G. gN g −1 = N for all g ∈ G. With this picture in mind, the following Lemma establishes that T M , and further shows that M is isomorphic to T R with R = O 2 , and T a normal subgroup of M . Lemma 1.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Though the overall system is not short-order Markov, each local model is.
Sentence 2: we show that the prediction for any test in a history of interest can be expressed as a prediction of a union test in T E. For the following, note that every history of interest h ∈ H I can be written as a corresponding sequence of bridging tests, which we will call s h . Also, we will use the subscript T E to distinguish predictions p T E (t|h) in T E from predictions p(t|h) in the original system.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To avoid this effect, we convert the presence of additive factors into multiplicative factors by augmenting the model with a latent "selector" variable, which is similar to that used for the "complete likelihood" in mixture models (Liu and Ihler, 2012).
Sentence 2: in the worst case, the size of the diagram still increases exponentially with the number of variables.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Instances of such bounds can be extracted, e.g., from [11] (Theorem 1), and from bounds discussed in [10].
Sentence 2: as was discussed in [6], in many cases our objective is to explore the entire risk-coverage trade-off, in other words, to get a pointwise bound on |f * (x)−f (x)|, i.e., individually for any test point x.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When the size of the behaviour data is small, the clustering performances of both DPM-BIRL and EM-MLIRL were not good enough due to the sparsity of data, hence their EVD results were similar to that of the baseline algorithm that independently runs BIRL on each trajectory.
Sentence 2: suppose that we would like to infer the reward function of a new trajectory after we finish IRL on the behaviour data consisting of M trajectories.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Relating back to the experimental data, we plot the probability of not observing the current stimulus for each type of 5-stimulus sequences in Figure 1 for (b) FBM and (c) DBM, since RT is known to lengthen with reduced stimulus expectancy.
Sentence 2: the new mean decision time is z+kb A tanh Az+Akb c 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: More specifically, we first use a coarse high probability upper bound on the queue-length (lemma 11) to get a first cut bound on the beginning of the regenerative cycle (lemma 12).
Sentence 2: we show that this "early stage" of the queueing bandit eventually gives way to a "late stage", where the optimal queue-regret scaling is O(1/t).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our algorithm can therefore be applied (1) to analyze the interplay of data set and kernel in a geometric fashion, (2) to help in model selection, and to (3) de-noise in feature space in order to yield better classification results.
Sentence 2: we define the relevant information vector as the vector  Proof The kernel PCA directions are given as (see [10]) and l k , u k being the eigenvalues and eigenvectors of the kernel matrix K. the kth PCA component for a point X j in the training set is The sum computes the jth component of Since the u k are orthogonal (K is a symmetric matrix), the projection of Y to the space spanned by the first d kernel PCA components is given by As we have just shown, the location of G is characterized by its scalar products with the eigenvectors of the kernel matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We first briefly describe them as follows: Threshold Average Precision Curve (TAPC) Although the ground-truth target value (i.e., the overlap rate of segment and bounding box) is a real value in the range of [0, 1], we can transform original prediction problem to a series of binary problems, each of which is conducted by thresholding the original groundtruth overlap rate.
Sentence 2: but this set of proposals may be very large, each proposal may be only partially correct (the correctness can be quantified by a continues value between 0 and 1 called "positiveness"), and several proposals may be required to obtain the correct label.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Using this we can write (16) as an unconstrained SOCP: (17 We can solve this problem in various ways, for example using interior-point methods for SOCP [8], which yield a worst-case complexity of O(n 3 ).
Sentence 2: we do not wish to solve the COP in this form, because we want to avoid using f or cp explicitly.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Research in cognitive psychology has consistently shown that humans represent everyday objects with a large number of features (e.g., [7,8]).
Sentence 2: the risk, defined as the expected 0-1 loss of the learner on a test instance, is R(t) ≡ E (x,y)∼p(x,y) E h∈V (t) 1 {h(x) =y} .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, the auxiliary variables are locally associated with each individual document, and this locality naturally allows us to develop a distributed sampler by splitting the documents into multiple subsets and allocating them to multiple machines.
Sentence 2: as a result, we obtained T = 350 for gCTM and T = 8 for vCTM, as pointed out with corresponing verticle line segments in Fig.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is tempting to posit that conv(F) = C holds more generally in the Bethe case.
Sentence 2: in the Bethe case with attractive potentials ✓, several recent results [22,19,18] establish that the Bethe approximation B(✓; ⇢) is an upper bound to the log partition function A(✓) when ⇢ lies in the spanning tree polytope, whereas B(✓; ⇢)  A(✓) when ⇢ = 1 F . By continuity, we must have B(✓; ⇢ ⇤ ) = A(✓) for some values of ⇢ ⇤ , and it would be interesting to characterize such values where the reweighted Bethe approximation is exact.
Relationship: neutral