sadat2307/MSciNLI huggingface dataset:
Domain: NeurIPS
Sentence 1: The flexibility in the choice of message passing algorithm makes it easy to consider several instantiations of the framework and use the one best suited to a particular problem.
Sentence 2: quantities about x s such as expected values under the pseudomarginal can be computed using the samples x (i) s . for any given variable node x s , the incoming messages to x s given in (4) are defined in terms of the importance weights and sampled values of the neighboring variables.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We then prove individual regret bounds for any sub-Gaussian distributions (similarly to Bubeck et al.
Sentence 2: theorem 3 The policy of Figure 3 has regret bounded as R n ≤ i:∆i>0 ∆ i + 80+log(∆i/ε) ∆i , uniformly in n. The proof of this result is fairly technical and it is deferred to the supplementary material.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Let X ⇢ R d be a domain such that we have an extension operator E of the form described in front of Theorem 1, P X be the uniform distribution on X and f 2 L 1 (X).
Sentence 2: [12] shows that the rate n /( +p) is often asymptotically optimal in a minmax sense.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In order to solve the relaxed convex optimization problem (8) efficiently at each round of the CCCP, we have designed a stochastic subgradient descent algorithm, using the Pegasos framework developed in [18].
Sentence 2: moreover, current MIL and MIML algorithms usually rely on a 'key' instance in the bag [1] or they transform each bag into single instance representation [25], while our algorithm makes an explicit effort to label every instance in a bag and to consider all of them during learning.
Relationship: neutral
Domain: NeurIPS
Sentence 1: One hopes that the manifold structure could be preserved in the much lower dimensional Euclidean space.
Sentence 2: a framework of semi-supervised learning based on differential operators can be formulated as follows: where C ∞ (M) denotes smooth functions on M, R 0 : R × R → R is the loss function and R 1 (f ) : C ∞ (M) → R is a regularization functional.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The Bethe Hessian systematically outperforms B and does almost as well as BP, which is a more complicated algorithm, that we have run here assuming the knowledge of "oracle parameters": the number of communities, their sizes, and the matrix p ab [5,4].
Sentence 2: we will therefore, somewhat improperly, call Hessian the matrix at the paramagnetic point: A more general expression of the Bethe Hessian in the case of weighted interactions atanh(w ij /r) (with weights rescaled to be in [0, 1]) is given by eq.
Relationship: neutral
Domain: NeurIPS
Sentence 1: This is accomplished by matrix factorization techniques such as independent component analysis [13], nonnegative matrix factorization [12] and (hierarchical) dictionary learning [4,3].
Sentence 2: the experiments in section 4.1 suggest that it may also be worthwhile to investigate the use of more parametric forms for the impulse response instead of the completely unbiased variant used here.
Relationship: neutral
Domain: NeurIPS
Sentence 1: When the signal of interest is known without uncertainty, the frequency representation can be obtained by means of the Fourier transform [6].
Sentence 2: the connection between temporal and frequency representations of GPs has aided the design of the GPs to have specific (prior) harmonic content in both parametric [25][26][27][28][29] and non-parametric [22,23] ways.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Significant plasticity in sensory cortical representations can be driven in mature animals either by behavioural tasks that pair sensory stimuli with reinforcement, or by electrophysiological experiments that pair sensory input with direct stimulation of neuromodulatory nuclei, but usually not by sensory stimuli presented alone.
Sentence 2: a mechanistic description alone neglects the information-processing aspects of the brain's function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Analyzing the most strongly correlated 75 pairs of neurons during the 180 minute recording (2-fold cross-validation) we find that the GBLM and Adaptive Filtering both increase model accuracy (Fig 4A).
Sentence 2: both the GBLM and Adaptive Filtering only increase the log likelihood relative to a homogeneous Poisson process by 3-4% for the parameters used here at the largest recording length.
Relationship: neutral
Domain: NeurIPS
Sentence 1: [17] proposed to use a specific stimulus decoding algorithm to classify trials that give accurate sensory information, and then quantify the increase in behavioral performance in the trials where the sensory decoding is correct.
Sentence 2: our intersection information measure I II (S; R; C) can also be used as a metric to discover and index brain areas that perform the key computations needed for perceptual discrimination, and thus turn sensory information into choice.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The OLS-UCB algorithm with parameter λ > 0 and f (t) = log t + (m + 2) log log t + m 2 log(1 + e λ ) enjoys for all times T ≥ 1 the regret bound where x stands for the smallest positive integer bigger than or equal to x.
Sentence 2: let G t = {A * µ ≥ A * μt + E t (A * )} be the event that the estimate of the optimal action is below its true mean by a big margin.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Next, we shall consider the problem of extending this approach to infinite-dimensional discrete distributions.
Sentence 2: the multiplicities representation significantly reduces the time and space complexity of our computations for most datasets, as we need only compute sums and products involving the number symbols with distinct frequencies (at most n max ), rather than the total number of symbols K. In practice, we compute all expressions not explicitly involving ⇡ using the multiplicities representation.
Relationship: neutral
Domain: NeurIPS
Sentence 1: They then showed how to solve the offpolicy evaluation problem by incorporating the causal bounds into the decision-making procedure.
Sentence 2: the reward is determined by values of: (1) the UCs governing the MUCT; (2) a set of unobserved variables (other than the UCs) where each affects an endogenous variable in the MUCT; and (3) the IB.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Nevertheless, we may obtain some evidence through Monte Carlo simulation.
Sentence 2: the signal energy is given by Substituting into the definition (3), the SNR is given by The minimum-to-average ratio of x is defined as Since x 2 /k is the average of {|x j | 2 | j ∈ I true }, MAR ∈ (0, 1] with the upper limit occurring when all the nonzero entries of x have the same magnitude.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The CVAE is composed of multiple MLPs, such as recognition network q φ (z|x, y), (conditional) prior network p θ (z|x), and generation network p θ (y|x, z).
Sentence 2: the parameters of the VAE can be estimated efficiently in the stochastic gradient variational Bayes (SGVB) [16] framework, where the variational lower bound of the log-likelihood is used as a surrogate objective function.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Future work should also consider whether the categorical principles we described (C1 through C5) are better characterized as probabilistic expectations.
Sentence 2: more formally, the independence principle specifies how the prior for the multiple object case is related to the prior p( v 1 ) on velocity fields for a single object (Equation 1): (2) We now develop a prior p( v) that incorporates probabilistic expectations about the motion of physical objects.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Once a CAP TCHA is broken (i.e., computer programs can successfully pass the test), bots can impersonate humans and gain access to services that they should not.
Sentence 2: training several different machine learning algorithms on different types of audio CAP TCHAs allowed us to analyze the strengths and weaknesses of the algorithms so that we could suggest a design for a more robust audio CAPTCHA.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Our method shows that tools from machine learning and Bayesian statistics allow us to leverage multiple resolutions of information to make accurate predictions with well-characterized uncertainties.
Sentence 2: note on priors For photometric weight and redshift inference, we use a flat prior on z n ∈ [0, 8], and empirically derived priors for m n and w n , from the sample of spectroscopically measured sources.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Note that planning is performed entirely in the latent state without access to any observations except for the depiction of the current state.
Sentence 2: we parametrize the transformation matrices and offset as vec where vec denotes vectorization and therefore vec To circumvent estimating the full matrix A t of size n z × n z , we can choose it to be a perturbation of the identity matrix A t = (I + v t r T t ) which reduces the parameters to be estimated for A t to 2n z .
Relationship: neutral
Domain: NeurIPS
Sentence 1: For the renewal process in which ISIs are drawn from a given distribution function, it is proven that the Fano factor is related to the ISI variability with F ≈ C 2 V [4].
Sentence 2: for the inference of λ(t) from {t i }, we use a prior distribution of x(t), such that the large gradient of x(t) is controlled by where the hyperparameter γ controls the roughness of the latent process x(t): with the small γ, the model requires a constant latent process, and vice versa.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In this paper we showed that for a general class of convex online learning problems, there always exists a distance generating function Ψ such that Mirror Descent using this function achieves a near-optimal regret guarantee.
Sentence 2: this includes the class F Lip which is the class of all functions with subgradients in X , and since F lin (X ) ⊂ F Lip (X ) we get the first equality.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Recalling that α ≥ 0, we have that sign(v j • x) = f (x) if and only if angle from v to x lies in (π/2, π/2 + α).
Sentence 2: . . , (x m , y m )} of labeled examples, the number of examples misclassified by the hypothesis sign(v • x) is a nonconvex function of v, and thus it can be difficult to find a v that minimizes this error (see [12,18] for theoretical results that support this intuition in various settings).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the following parts of the paper, we define the likelihood ratio distance between x and y as the square root of the negative logarithm of the similarity: ) It is worth pointing out that, for arbitrary distributions p(x), d(x, y) is not necessarily a distance metric as the triangular inequality may not hold.
Sentence 2: table 2 shows the 99% FPR on the data without jitter effects 2 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: The figures show that the robustly regularized risk provides a different type of protection against overfitting than standard regularization or constraint techniques do: while other regularizers underperform in heavily constrained settings, the robustly regularized estimator b ✓ rob n achieves low classification error for all values of ⇢.
Sentence 2: := argmin ✓ R(✓) = 0, which satisfies R(✓ ? )
Relationship: neutral
Domain: NeurIPS
Sentence 1: For data y ∈ R n , isotonic regression seeks to minimize 1 2 y − β 2 2 subject to the condition that the β i are non-decreasing.
Sentence 2: the gradient and second differential of L(β | y, X) amount to As an example, when ψ(θ) = θ 2 /2 and c 2 (τ ) = τ 2 , the density (1) is the Gaussian likelihood, and GLM regression under the identity link coincides with standard linear regression.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We consider undirected, weighted graphs G = (V, E) with n vertices.
Sentence 2: denoting by H ij the expected hitting time, by C ij the commute distance between two vertices v i and v j and by d i the degree of vertex v i we prove that the hitting times and commute distances can be approximated (up to the constant vol(G) that denotes the volume of the graph) by The intuitive reason for this behavior is that if the graph is large, the random walk "gets lost" in the sheer size of the graph.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Even with large batches, each new instance still requires collapsing the uncertainty around the instance-specific parameters in order to quickly perform well on the task.
Sentence 2: the HiP-MDP paradigm introduced a low-dimensional latent task parameterization w b that, combined with a state and action, completely describes the system's dynamics T (s |s, a, w b ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: In general, there is no value a v that maximizes θ v (a v , a −v ) independently of the opponent's choice of a −v .
Sentence 2: as a consequence of Theorem 2, we can identify the unique Nash equilibrium of the game with cost functions θ +1 and θ −1 , if it exists, by finding the minimax solution of the game with joint cost function θ 0 .
Relationship: neutral
Domain: NeurIPS
Sentence 1: We take 1) and add random effects as follows: (4) Each group j has its own component mean u jk for the kth component and these group-level parameters come from a common prior distribution N (µ k , τ 2 k ).
Sentence 2: given a template mixture of two components with parameters θ a and θ b , in hierarchical DPs a mixture model for each group can have m a and m b exact copies (commonly known as tables in the Chinese restaurant process representation) of each of the two components in the template-thus, there is no notion of random variation in component parameters across groups.
Relationship: neutral
Domain: NeurIPS
Sentence 1: As AI systems become more powerful and autonomous, these failures will become more frequent and grave as RL agents exceed human performance, operate at time-scales that forbid constant oversight, and are given increasingly complex tasks -from driving cars to planning cities to eventually evaluating policies or helping run companies.
Sentence 2: let V π R (s) be the expected return of reward function R from state s, given that the agent follows policy π.
Relationship: neutral
Domain: NeurIPS
Sentence 1: While we prove that the learning bounded vertex cover Bayesian network structures can be done in polynomial time, the unavoidable dependence on k in the degree the polynomial makes the algorithm of our main theorem infeasible for practical usage when the vertex cover number k increases.
Sentence 2: we report the score for the optimal DAG without structure constraints, and for the optimal DAGs with bounded tree-width and bounded vertex cover when the bound k changes, as well as the running time required for finding the optimal DAG in each case.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Suppose that Then there exists a factorization of 2 R m⇥k is an orthonormal matrix, and satisfies kU The proof of Lemma 4.6 is provided in Appendix B.5.
Sentence 2: the proof of Theorem 3.4 for alternating gradient descent and gradient descent, and related lemmas are provided in the appendix.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Throughout the rest of this section, we impose an additional assumption that the distribution D is finitely supported: IIxl12 :s M almost everywhere with respect to the measure D. From Section 3.1, we know that for any sufficiently small positive number A, Ilw.w.
Sentence 2: for problems that are numerical in natural, the potential parameter space can be significantly reduced by using the first order condition of the optimal solution.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Interestingly, the truncation procedure in the gradient stage turns out to be useful in avoiding spurious stationary points in the context of nonconvex optimization.
Sentence 2: even though the truncated spectral initialization improves upon the "plain vallina" spectral initialization, its performance still suffers when the number of measurements is relatively small and its advantage (over the untruncated version) narrows as the number of measurements grows.
Relationship: neutral
Domain: NeurIPS
Sentence 1: We take the notion that ACh influences the balance of bottom-up and top-down one step further, suggesting that in the hierarchical cortex consisting of several processing stages, ACh could mediate this balance at any stage.
Sentence 2: as long as there is some input, even if it is unspecific noise, hallucinations can be formed, but losing the input completely might require too much of a bias shift.
Relationship: neutral
Domain: NeurIPS
Sentence 1: It is worth noting that oracle complexity measures only the number of queries to the oracle-for instance, the number of (approximate) function or gradient evaluations.
Sentence 2: convex optimization is the task of minimizing a convex function f over a convex set S ⊆ R d . Assuming that the minimum is achieved, it corresponds to computing an element x * f that achieves the minimum-that is, x * f ∈ arg min x∈S f (x).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Unlike existing work which creates dependencies across multiple DPMG through exact or perturbed sharing of mixture components or through sharing of the entire mixture model, proposed I 2 GMM model associates each cluster with a distinct atom of the higher level DP through centering of the base distribution of the corresponding DPMG at that atom.
Sentence 2: there are a total of seventeen Gaussian components, four clusters, and 17,000 instances (1000 instances per component) in this data set.
Relationship: neutral
Domain: NeurIPS
Sentence 1: One possible construction algorithm is an extension of Kruskal's algorithm for the MST where we pick edges without replacement and restart for every new tree.
Sentence 2: for T = 1 this gives the MST of the unperturbed data set; for T → ∞ it gives a stochastic graph where e ij is the probability (in the Laplace sense) of that edge under the noise model.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Assume for a moment that Figure 1: The figure on the left shows the sequence of states along an optimal path beginning at a single-cluster configuration and ending at the MAP configuration (F1 scores for each state are shown).
Sentence 2: the reward function used is the residual improvement based on the performance metric F when the system transitions between states s and s : this reward can viewed as learning to minimize the geodesic distance between a current state and the MAP configuration on the proposal manifold.
Relationship: neutral
Domain: NeurIPS
Sentence 1: The scalar (inner) product of two vectors x and y in the n-dimensional real space ℜ n will be denoted by x ′ y and the 2-norm of x will be denoted by x .
Sentence 2: first, notice that (by negation) the feasibility constraints in (1) can also be defined as: a solution w is feasible iff there exist no pair of samples from the two classes such that f w ( ) orders them incorrectly.
Relationship: neutral
Domain: NeurIPS
Sentence 1: In the first style of evaluation, we compared the performance of our classifiers against the Known Hypernym versus Known Non-Hypernym labels assigned by 1 The corpus contains articles from the Associated Press, Wall Street Journal, and Los Angeles Times, drawn from the TIPSTER 1, 2, 3, and TREC 5 corpora [7].
Sentence 2: there has been significant recent interest in finding methods for automatically learning taxonomic relations and constructing semantic hierarchies.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Then the selections in steps (S2) and (S3) are done in time O(1).
Sentence 2: regret bounds for these algorithms do not scale as well with the number of arms: even if the tree widths are given, then letting ∆ min min x∈X: ∆(x)>0 ∆(x), the regret bound is proportional to |X δ |/∆ min (where X δ is as in Definition 1.1), whereas the regret bound in Theorem 2.3 is (essentially) in terms of the covering numbers N cov δ/8 (X δ ).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Even though we have simplified the state space by partitioning by user, the state space for a single user remains sufficiently complex to preclude standard table-based representation of value functions (also, each user's state space is effectively infinite, as there are real-valued state features).
Sentence 2: the Living Room is a central public place, frequented both by many regulars, and by users new to LambdaMOO.
Relationship: neutral
Domain: NeurIPS
Sentence 1: For each k ∈ [N ], the distribution P t,k over labeled examples that is given to the k-th run of the weak learner is as follows: a draw from P t,k is made by drawing (x, f (x)) from P and accepting (x, f (x)) as the output of the draw from P t,k with probability p x = α t,k (h 1,1 (x), .
Sentence 2: in the t-th stage of boosting the weak learner is run N times in parallel.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Though there has been significant work on PAC RL algorithms for the infinite horizon setting, there has been relatively little work on the finite horizon scenario.
Sentence 2: a key idea is that in order to obtain accurate estimates of the value function of a policy from a starting state, it is sufficient to have only a loose estimate of the parameters of (s, a)-pairs that are unlikely to be visited under this policy.
Relationship: neutral
Domain: NeurIPS
Sentence 1: To classify the green nodes, we will use the matrix A (g) = (A vw ) v,w∈V (g) , as well as the graph of indirect edges.
Sentence 2: we focus here on scenarios where the network size can be extremely large (online social and biological networks can, already today, easily exceed several hundreds of millions of nodes), so that the adjacency matrix A of the corresponding graph can become difficult to manipulate and store.
Relationship: neutral
Domain: NeurIPS
Sentence 1: Richard E. Turner is supported by Google as well as EPSRC grants EP/M0269571 and EP/L000776/1.
Sentence 2: although heuristics could be introduced to break up the clumps, this result suggests that using small α values for online inference and learning might be more appropriate (this recommendation differs from the batch setting where intermediate settings of α around 0.5 are best [13]).
Relationship: neutral
Domain: NeurIPS
Sentence 1: Moreover, the activities in various levels of the hierarchy resemble electrophysiologically recorded activities in the visual cortical neurons during attentional modulation and perceptual discrimination, lending farther credence to the particular encoding and computational mechanisms that we have proposed.
Sentence 2: this spans a broad spectrum, from distributional codes that can also encode restricted aspects of uncertainty [1] to more exotic interpretations of codes as representing complex distributions [1,2,3,4,5].
Relationship: neutral
Domain: NeurIPS
Sentence 1: From a top-down view, the model can be considered as a stochastic feedforward network (Tang and Salakhutdinov, 2013), where the input matrix in Φ (T ) , the output matrix is Φ (1) , and the stochastic units are drawn from the Dirichlet distribution.
Sentence 2: for example, one commonly-used prior for TP and WD is a Dirichlet distribution, as in Latent Dirichlet Allocation (LDA) (Blei et al., 2003).
Relationship: neutral
Domain: NeurIPS
Sentence 1: [15], we formulate the Spatial-Model as an MRF-like model over the distribution of spatial locations for each body part.
Sentence 2: for datasets that cover a larger range of the possible poses (for instance the LSP [17] dataset), we would expect these distributions to be less tightly constrained, and therefore this simple Spatial-Model will be less effective.
Relationship: neutral