sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: As such, even though we specify a prior on partitions with 2 L−1 − 1 changepoints, the resulting functions can appear to adaptively use fewer by averaging over the uncertainty in the discontinuity location.
Sentence 2: the acceptance rate tends to decrease as higher posterior probability partitions A are discovered, especially for trees with many levels and large input spaces X for which the search space is larger.
Relationship: neutral
Domain: NeurIPS
Sentence 1: M. Define q(x, z) = p(x)q(z | x), where q(z | x) is a fixed inference model.
Sentence 2: it is often overlooked that an overly-expressive inference model can be detrimental to the test set performance of both the amortized posterior approximator and, more importantly, the generative density estimator.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The model simply cannot assume highly unlikely stances-these are either not representable at all, or have reduced probability-and thus avoids compensatory, unrealistic body proportion estimates.
Sentence 2: factor analysis is too limited to be of practical use, and GTM-while flexible-has two important practical problems: (1) the latent space must be discretised to allow tractable learning and inference, which limits it to very low (2-3) latent dimensions; (2) the parameter estimation is prone to bad local optima that result in highly distorted mappings.
Relationship: neutral
Domain: NeurIPS
Sentence 1: (States are assigned values of RVs.)
Sentence 2: the pdf in (3) can be treated as a probability mass function (pmf) over s ∈ κ(σ (i) (1 : t − 1)) and sampling from it becomes equivalent to sampling Hence, we can interpret a particle x (i) σ(1:t−1) as a sequence of indices of selected graph vertices σ(1:t−1) is a vector of ones assigned to RVs with indices in σ (i) (1 : t − 1).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our approach begins with the augmented bases used in CBP, but adds basis vectors greedily, drawing on the well known Orthogonal Matching Pursuit algorithm [11].
Sentence 2: cBP (with a Taylor basis) recovers coefficients using: Here we denote by F the matrix with columns {f n,j (t)} and F the matrix with columns {f n,j (t)}.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As we show in this paper, alpha-divergences have the disadvantage of inducing high-variance gradients, since the ratio between posterior and variational distribution enters the bound polynomially instead of logarithmically.
Sentence 2: this expenses some tightness of the bound but makes the method more flexible by allowing us to optimize over V 0 as well, as we describe next.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this section, we present the result of simulations comparing the monotone algorithm and our algorithm PFS r . The experiments were carried out as follows: given a buyer's valuation v, a discrete set of false valuations v were selected out of the set {.03, .06, . . . , v}.
Sentence 2: for this setting, the buyer would no longer have an incentive to lie, thus, an algorithm such as binary search would achieve logarithmic regret, while the regret achieved by the monotone algorithm is only guaranteed to be in O( One may argue that the monotone algorithm is too specific since it admits a single parameter β and that perhaps a more complex algorithm with the same monotonic idea could achieve a more favorable regret.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As concrete examples, we show two screening methods SIS and HOLP are both strong screening consistent (subject to additional constraints) with large probability if n > O((ρs+σ/τ ) 2 log p) under random designs.
Sentence 2: letting C = X T X/n and β be a given coefficient vector, the IC is expressed as for some θ > 0, where C A,B represents the sub-matrix of C with row indices in A and column indices in B.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Due to the fact that the cost function of MMP is piecewise defined, one cannot find a closed-form relation between ∆w and ∆v π .
Sentence 2: a strong assumption considered in IRL-based al- gorithms is that the reward is a linear function of state-action features, and the frequencies of these features can be estimated from a few demonstrations even if these demonstrations cover only a small part of the state space.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then for γ > 0 and a fixed probability of error δ ∈ (0, 1), we have P G = Ĝ ≥ 1−δ, provided that m ∈ O( 1 γ 2 ln n + ln r δ ) interventional samples are used per δ-noisy path query in Algorithm 5.
Sentence 2: we consider an experiment as the actual setting of values to the variables.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For SELU parameters α = α 01 and λ = λ 01 , we show in the next theorem that if (ω, τ ) is close to (0, 1), then g still has an attracting and stable fixed point that is close to (0, 1).
Sentence 2: we have introduced self-normalizing neural networks for which we have proved that neuron activations are pushed towards zero mean and unit variance when propagated through the network.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is explained by the fact that in Causal InfoGAN, Q is only trained on generated observations, and can overfit to generated images.
Sentence 2: to evaluate planning performance, we hand-coded an oracle function that evaluates whether an observation trajectory is feasible or not (e.g., does not cross obstacles, correctly reports ∅ when a trajectory does not exist).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Each categorical input attribute was converted into n binary attributes by a 1-of-n encoding (where n is the attribute's arity).The post-processed versions of these datasets are at http://www.cs.cmu.edu/∼awm/kns 1.
Sentence 2: each experiment required R k-NN classification queries (where R is the number of records in the dataset) and each query involved the k-NN among 0.9R records.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Using the law of total probability, we have the following equation for the filtering distribution: We can think of the integral in (5) as a sum over a distribution of experts, where each expert corresponds to a single pose history, u 1:t−1 .
Sentence 2: for each expert we could then use Kalman filtering equations to infer the posterior distribution of texture given the observed images.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recent advances that exploit the capacity and flexibility in this approach have expanded what kinds of models can be trained.
Sentence 2: * For clarity of presentation, we will often omit dependence on parameters φ of the generative model, so that p(x, h) = p(x, h; φ) Variational methods have surpassed traditional methods such as Markov chain Monte Carlo [MCMC,15] and mean-field coordinate ascent [25] as the de-facto standard approach for training directed graphical models.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, after n observations and with the proper step-sizes, averaged SGD achieves the rate of O(1/µn) in the strongly-convex case [5,4], while it achieves only O(1/ √ n) in the nonstrongly-convex case [5], with matching lower-bounds [8].
Sentence 2: a crucial point is that for machine learning scenarios where f n is a loss associated to a single data point, its complexity is only twice the complexity of a regular stochastic approximation step, since, with f n (θ) = ℓ(y n , x n , θ ), f ′′ n (θ) is a rank-one matrix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that Theorem 2 does not in any way indicate what is the best non-factorial reweighting scheme in practice (for example, in our limited experience with empirical simulations, the selection α → 0 is not necessarily always optimal).
Sentence 2: for example, with α small, the penalty g SBL (x) is more highly concave favoring sparsity, while in the limit at α becomes large, it acts like a standard 1 norm, still favoring sparsity but not exceedingly so (the same phenomena occurs when using the penalty ( 11)).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Any optimization method can be envisioned to minimize J ν .
Sentence 2: from the basic properties of the Bellman operator, for any policy π we have that T * v π ≥ v π . Consequently, the ν-weighted 1 -norm of the residual is indeed the expected Bellman residual: there is naturally no bias problem for minimizing a residual here, contrary to other residual approaches [1].
Relationship: neutral
Domain: NeurIPS
Sentence 1: In general, it is not easy to quantify the difference to the lower bound of Lai and Robbins lim inf Even for Gaussian distributions, there is no general closed-form formula for T * (µ) and w * (µ) except when K = 2.
Sentence 2: denoting d(µ, µ ) = KL(ν µ , ν µ ) the Kullback-Leibler divergence between two distributions parameterised by µ and µ , they provide results which can be adapted to obtain the following bound.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The last operation is a task-specific 1 × 1 convolution to yield a width K t adapted to the task t. When learning from multiple auxiliary tasks, the first two layers of the encoder are shared to have a common encoder trunk with task-specific heads, further reducing computation.
Sentence 2: design of this component has not been fully explored and further experiments should yield better results.
Relationship: neutral
Domain: NeurIPS
Sentence 1: That is, in the case of c → ∞, the objective in (1) is a monotonically decreasing function of a.
Sentence 2: the vertical blue and red lines denote an "ambiguous region" around the decision boundary; objects to the left of the blue line have the label "not graspable;" those to the right of the red line are labeled as "graspable," and objects between these lines could have labels in mixed order.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This experiment does not satisfy ε-differential privacy for any fixed value of ε, since there is no fixed maximum number of rounds for which the experiment will run (for a fixed number of rounds, a simple composition theorem, Theorem 2.5, shows that the ε-guarantees in a sequence of computations "add up.")
Sentence 2: our empirical results show that the active, ex-post privacy approach massively outperforms inverting the theory curve, and also improves on a baseline "ε-doubling" approach.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then, we can treat the input bag-of-words as a |x|-trials multinomial sample from that distribution and use as the reconstruction loss its negative log-likelihood: We now must ensure that the decoder can compute p( x = x i |φ(x)) efficiently from φ(x).
Sentence 2: first, the encoder representation will now involve a sum of the representation of all words, reflecting the relative frequency of each word: Moreover, decoder training will assume that, from the decoder's output, we can obtain a probability distribution p( x|φ(x)) over any word x observed at the reconstruction output layer.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Often, the distributions used in these models are difficult to sample from, being defined over large state spaces or having unknown normalization constants.
Sentence 2: these differences were statistically significant, with a one-tailed Student's t-test for independent samples giving t(38) = 7.36, p < 0.001 and t(38) = 2.01, p < 0.05 for µ and σ respectively.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Specifically, to enable GAIL to produce diverse solutions, we condition the discriminator on the embeddings generated by the VAE encoder and integrate out the GAIL objective with respect to the variational posterior q (z|x 1:T ).
Sentence 2: we first demonstrate the effectiveness of our VAE architecture and investigate the nature of the learned embedding space on a reaching task with a simulated Jaco arm.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Although different sampling techniques could be used in principle [15], our goal is to model correlations between each variable X uv and some neighboring region G uv in G. Such a neighborhood should be large enough to make ∆λ 2 (u, v, G uv ) sufficiently informative with respect to the overall network, but also small enough to keep the spectral decomposition of G uv computationally tractable.
Sentence 2: the proposition follows straightforwardly from Lemma 1, given that We now proceed to define FRFs.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Locally Linear Embedding (LLE, [3]) and Laplacian Eigenmaps (LE, [4]) can be viewed as Laplacian operator based methods which mainly consider the local neighborhood structure of the manifold.
Sentence 2: for any vector a ∈ R m , we have P i a ∈ T xi M and (a − P i a) ⊥ P i a.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To maintain bounded staleness while minimizing wait times on read row() operations, SSPtable uses the following cache protocol: Let every table-row in a thread or process cache be endowed with a clock r thread or r proc respectively.
Sentence 2: in SSP, workers can make updates to a parameter 1 ✓, where the updates follow an associative, commutative form ✓ ✓ + .
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is due to examples where the random draws of lead to function values ¡ © $ that are consistent with much longer length scale than the true function; the mean prediction becomes somewhat inaccurate, but worse still, the inferred variance becomes very small (because a very slowly varying function is inferred), leading to very poor performance compared to SMC.
Sentence 2: a point in a sparse region is far more informative about the shape of the function for BMC than points in already densely sampled areas.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the matrix factorization task using U oI CU R , reconstruction accuracy was the Frobenius norm of the difference between the data matrix A and the low-rank approximation matrix A constructed from A(:, c), the reduced column matrix of A: A − A F , where c is the set of k selected columns.
Sentence 2: neither should be too large, and their relative values express the balance between feature compression and expansion.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Similar to Subsection 3.1, a naive way to apply the MC method to a network is as follows: Let 0 ⇡ := {|( B⇡ ) m,n |, ( ⌦⇡ ) m,m ; 1  m  n  p}, and for any pair of domains ].
Sentence 2: for variable E and any set S, if , then S is not the parent set of E. Similarly, the authors of [WSBU18] consider the case that a (i) 6 = a (j) and either E . under this assumption, in this case for variable X 2 {C, E} and set , then S is the parent set of X.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The intuition of incorporating the triggering probability p D,S i to modulate the 1-norm condition is that, when an arm i is unlikely triggered by action S (small p D,S i ), the importance of arm i also diminishes in that a large change in µ i only causes a small change in the expected reward r S (µ).
Sentence 2: in the disjunctive form the player stops when the first 1 is revealed and she gains reward of 1, or she reaches the end and gains reward 0.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We performed extensive experimental analysis to understand the proposed M-Walk algorithm, including (i) the contributions of different components, (ii) its ability to overcome sparse rewards, (iii) hyperparameter analysis, (iv) its strengths and weaknesses compared to traditional KBC methods, and (v) its running time.
Sentence 2: compared to the policy gradient method (PG-Walk), and Q-learning method (Q-Walk) methods under the same model architecture, M-Walk with MCTS is able to generate trajectories with more positive rewards, and this continues to improve as training progresses.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This interpretation provides an insight into the non-optimal stationary points of the convex max-product, i.e., points for which it is not able to generate consistent beliefs b α (x α ) when it iterates over i = 1, . . . , n. The representation of the subdifferential as the amount of disagreement between the marginalization constraints provides a simple procedure to verify dual optimality, as well as to construct primal optimal solutions.
Sentence 2: it uses a double loop scheme where every update involves executing a convex sum-product algorithm.
Relationship: neutral
Domain: NeurIPS
Sentence 1: A factored, n-agent Dec-POMDP is a Dec-POMDP such that the system state can be factored into n + 1 distinct components, so that S = S 0 × S 1 × • • • × S n , and no state-variable appears in any S i , S j , i = j.
Sentence 2: there exists a functional mapping, J : In a Dec-MDP, then, the sum total of the individual agent observations provides a complete picture of the state of the environment.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We begin by using a result from [2] that classical mean-shift (using a flat kernel) is equivalent to finding the local maxima of the following density estimate: In standard mean-shift, d is the Euclidean distance function, b is a constant that controls the kernel bandwidth, and z(b) is a normalization constant.
Sentence 2: there is still much room for improvement in weaklysupervised element discovery algorithms.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Apart from being a non-convex problem, the matrix factorization studied in the present paper is further complicated by the {0, 1}-constraints imposed on the left factor T , which yields a combinatorial optimization problem that appears to be computationally intractable except for tiny dimensions m and r even in case the right factor A were already known.
Sentence 2: algorithm 4 is impractical as a stand-alone scheme, because without proper initialization, it may take many iterations to converge, with each single iteration being more expensive than Algorithm 3.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, these methods utilize a fundamentally different stochastic gradient information: they have access to an unbiased gradient estimator.
Sentence 2: algorithm 2: ASEGA: Accelerated SEGA 1 Initialize: Sample S k = I S k , where S k ⇠ S, and compute g k , h k+1 according to (4), ( 6) The method and analysis is inspired by [2].
Relationship: neutral
Domain: NeurIPS
Sentence 1: Conditional on all parameters, H C and H T are independent.
Sentence 2: we thus obtain the final components of our hierarchical model: In order to apply PAC, we must specify a nucleotide substitution model, that is, the probability that a nucleotide i mutates to a nucleotide j over evolutionary distance t. In the above, η parametrizes this model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: If s is constant across stimulus strengths, the other two parameters of the model must explain differences in behaviour, between stimulus strengths, by taking on values that depend on stimulus strength.
Sentence 2: a high coherence RDM stimulus has a large proportion of motion in the correct direction with very low variability of measurements whereas a low coherence RDM stimulus tends to have lower proportions of motion in the correct direction, with high variability (cf.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Surprisingly, the hierarchical baselines (HSVM,TD and OT) experience a very large drop in performance on LSHTC-small when compared to the flat baselines, indicating that the hierarchy information actually mislead these methods rather than helping them.
Sentence 2: formally, the generative model for M1 is The parameters of the root node are drawn using user specified parameters w 0 , Σ 0 , a 0 , b 0 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is more robust against overfitting, and thus we are able to use very flexible models (such as deep neural networks) given limited P data.
Sentence 2: the replacement of π p with some π p > π p introduces additional bias of R pu (g) in estimating R(g), but it also pushes R pu (g) away from R pu (g) and then pushes nnPU away from uPU.
Relationship: neutral
Domain: NeurIPS
Sentence 1: From here, we will apply the confidence set results from Section 5 to obtain our regret bounds.
Sentence 2: let A = {R ú , R k oe R k 'k} and B = {P ú , P k oe P k 'k} and condition upon these events to give: The posterior sampling lemma ensures that 1≠8" by a union bound on {A c fi B c }.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is because (i) the reference predictors do not need it; and (ii) if we did include the cost of observing the loss function for the reference predictors, then the loss of each predictor would just be increased by c d+1 T , and so the regret R T would just be reduced by c d+1 T , making it substantially easier for the learner to achieve sublinear regret.
Sentence 2: the standard "batch learning" framework has a pure explore phase, which gives the learner a set of labeled, completely specified examples, followed by a pure exploit phase, where the learned predictor is asked to predict the label for novel instances.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We then reformulate the sparse PCA optimization problem to explicitly reflect the maximum additional variance objective on each round.
Sentence 2: the conditional variance is the Schur complement of the vector variance x T Σx in the full covariance matrix V . By substituting sample covariance matrices for their population counterparts, we arrive at a new deflation technique: Schur complement deflation Schur complement deflation, like projection deflation, preserves positive-semidefiniteness.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We find a consistent contribution of AoA to naming latency, as well as the conditions under which there is an independent contribution from frequency in some tasks.
Sentence 2: still more recent studies question this finding and find that both AoA and frequency are significant and contribute independently to naming latency (Ellis & Morrison, 1998;Gerhand & Barry, 1998,1999.
Relationship: neutral
Domain: NeurIPS
Sentence 1: There are also other applications of GCD, such as non-negative matrix factorization [11], large-scale linear SVM [29], and [8] proposed an approximate way to select variables in GCD.
Sentence 2: each GCD update only costs O(`) using this trick of maintaining g. for solving kernel SVM, GCD is faster than SCD and CCD since there is no additional cost for selecting the best variable to update.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Meanwhile, it reduces the memory requirement from O(md) to O(m 2 ) where d could be billion-scale but m is often less than 10.
Sentence 2: when we increase the feature number to 512M, the L-BFGS fails with an out-of-memory exception, while VL-BFGS can easily scale to 1B features.All of these clearly show the scalability advantage of VL-BFGS over traditional L-BFGS.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Strikingly, by proper adjustments of these normalizations, we were able to train various complicated models without hurting the classification performance.
Sentence 2: for a layer with d−dimensional input x = (x (1) , x (2) , ..., x (d) ), L ∞ batch normalization normalize each dimension where µ k is the expectation over x (k) , n is batch size and C L∞ (n) is computed similarly to C L1 (n) (derivation appears in appendix).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Indeed, the original purpose of Resolving was not to improve upon a blueprint strategy in a subgame, but rather to compactly store it by keeping only the EV at the root of the subgame and then reconstructing the strategy in real time when needed rather than storing the whole subgame strategy.
Sentence 2: 1 For example, a better strategy for P 2 would be to choose Heads with probability 3 4 and Tails with probability 1 4 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: Observe that, by the hypothesis on t , we have z t ≤ L x t . We first consider two cases, based on the norm of θ t . Case 1: With this assumption, and using the third property of Lemma 2, we have We now use the second statement of Lemma 1.
Sentence 2: we derive the Dimension-Free Exponentiated Gradient from the general OMD above.
Relationship: neutral