The rapidly expanding artificial intelligence (AI) industry has produced diverse yet powerful prediction tools, each with its own network architecture, training strategy, data-processing pipeline, and domain-specific strengths. These tools create new opportunities for semi-supervised inference, in which labeled data are limited and expensive to obtain, whereas unlabeled data are abundant and widely available. Given a collection of predictors, we treat them as a mixture of experts (MOE) and introduce an MOE-powered semi-supervised inference framework built upon prediction-powered inference (PPI). Motivated by the variance reduction principle underlying PPI, the proposed framework seeks the mixture of experts that achieves the smallest possible variance. Compared with standard PPI, the MOE-powered inference framework adapts to the unknown performance of individual predictors, benefits from their collective predictive power, and enjoys a best-expert guarantee. The framework is flexible and applies to mean estimation, linear regression, quantile estimation, and general M-estimation. We develop non-asymptotic theory for the MOE-powered inference framework and establish upper bounds on the coverage error of the resulting confidence intervals. Numerical experiments demonstrate the practical effectiveness of MOE-powered inference and corroborate our theoretical findings.

At least nine people, including two children, were killed in Israeli strikes in southern Lebanon on Thursday, the health ministry said, as violence continues despite a ceasefire now in its second week. The strikes - which Israel said were targeting Hezbollah infrastructure - also wounded 23 people, among them eight children and seven women, the ministry said. Separately, Hezbollah said it had carried out attacks on Israeli forces in the south, including a drone strike targeting soldiers in the Bint Jbeil district. The violence comes as Israel presses ahead with military operations in Lebanon despite the ceasefire announced on 16 April, after direct talks between Lebanese and Israeli ambassadors in Washington. Lebanese President Joseph Aoun criticised what he described as continuing Israeli violations of the truce, saying strikes and demolitions of homes and places of worship were ongoing despite the ceasefire.

We consider the problem of nonnegative submodular maximization in the online setting. At time step t, an algorithm selects a set St C 2V where C is a feasible family of sets. An adversary then reveals a submodular function ft. The goal is to design an efficient algorithm for minimizing the expected approximate regret. In this work, we give a general approach for improving regret bounds in online submodular maximization by exploiting "first-order" regret bounds for online linear optimization. For monotone submodular maximization subject to a matroid, we give an efficient algorithm which achieves a (1 c/e ε)-regret of O( p kTln(n/k)) where n is the size of the ground set, k is the rank of the matroid, ε > 0 is a constant, and cis the average curvature. Even without assuming any curvature (i.e., taking c = 1), this regret bound improves on previous results of Streeter et al. (2009) and Golovin et al. (2014). For nonmonotone, unconstrained submodular functions, we give an algorithm with 1/2-regret O( nT), improving on the results of Roughgarden and Wang (2018). Our approach is based on Blackwell approachability; in particular, we give a novel first-order regret bound for the Blackwell instances that arise in this setting.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

In this section, we shall show detailed derivations for the point-wise dependency estimation methods. Four approaches are discussed: Variational Bounds of Mutual Information, Density Matching, Probabilistic Classifier, and Density-Ratio Fitting. For convenience, we define Ω = X Y. We have PX,Y and PXPY (can also be written as PX PY) be the probability measures over σ algebras over Ω with their probability densities being the Radon-Nikodym derivatives (i.e., p(x,y) = dPX,Y/dµ and p(x)p(y) = dPXPY/dµwith µbeing the Lebesgue measure). These estimators have the logarithm of point-wise dependency (PMI) as the intermediate product, which we will show in the following. We denote Mbe any class of functions m: Ω R. Proposition 1 (INWJ and its neural estimation, restating Nguyen-Wainwright-Jordan bound [5, 18]).

Few-shot classification aims to recognize unlabeled samples from unseen classes given only few labeled samples.