We resolve a 30-year-old open problem concerning the power of unlabeled data in online learning by tightly quantifying the gap between transductive and standard online learning. In the standard setting, the optimal mistake bound is characterized by the Littlestone dimension dof the concept class H(Littlestone, 1987). We prove that in the transductive setting, the mistake bound is at least Ω d . This constitutes an exponential improvement over previous lower bounds of Ω(loglog(d)), Ω p log(d), and Ω(log(d)), due respectively to Ben-David, Kushilevitz, and Mansour (1995, 1997), and Hanneke, Moran, and Shafer (2023). We also show that this lower bound is tight: for every d, there exists a class of Littlestone dimension d with transductive mistake bound O d . Our upper bound also improves upon the best known upper bound of (2/3) d from Ben-David et al. (1997). These results establish a quadratic gap between transductive and standard online learning, thereby highlighting the benefit of advance access to the unlabeled instance sequence. This contrasts with the PAC setting, where transductive and standard learning exhibit similar sample complexities.

It's a trait evolution forgot to get rid of. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. A colorized film still from the 1931 German film'Emil and the Detectives' shows a man sleepwalking. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

In this section we provide a detailed proof for the correctness and completeness of the ICD algorithm. For easier referencing we describe ICD in Algorithm 1, and describe the ICD-Sep conditions. A set Zis a subset of ICD-Sep(A,B) given r {0,...,|O| 2}, if and only if 1. |Z|= r, 2. Z Z, there exists a PDS-path ΠB(A,Z) such that, (a) |ΠB(A,Z)| r and (b) every node on ΠB(A,Z) is in Z, and 3. Z Z, node Z is a possible ancestor of Aor B (not a necessary condition). Denote A,B a pair of nodes from O that are connected in G and disconnected in D, and such that Ais not an ancestor of B in D. If A B |[Z0] S, where Z0 O is a minimal separating set having size n+ 1, then there exists a subset Z O having the same size of n+ 1 such that that A B |Z S, and for every node Z Zthere exists a PDS-path ΠB(A,Z) in G, such that every node V on the PDS-path is also in Z. Proof. It was previously shown that a minimal separating set for Aand B, where Ais not an ancestor of B, is a subset of D-Sep(A,B) (Spirtes et al., 2000, page 134 and Theorem 6.2; Spirtes et al., 1999).

We consider running multiple instances of multi-armed bandit (MAB) problems in parallel. A main motivation for this study are online recommendation systems, in which each of N users is associated with a MAB problem and the goal is to exploit users' similarity in order to learn users' preferences to K items more efficiently. We consider the adversarial MAB setting, whereby an adversary is free to choose which user and which loss to present to the learner during the learning process. Users are in a social network and the learner is aided by a-priori knowledge of the strengths of the social links between all pairs of users. It is assumed that if the social link between two users is strong then they tend to share the same action.

The kraken-like apex predators were smart, too. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. The fossils prove octopuses existed at least 5 million years earlier than originally thought. Breakthroughs, discoveries, and DIY tips sent six days a week. Around 100 million years ago, real kraken-like creatures stalked Earth's prehistoric oceans.

The correlation between events is ubiquitous and important for temporal events modelling. In many cases, the correlation exists between not only events' emitted observations, but also their arrival times. State space models (e.g., hidden Markov model) and stochastic interaction point process models (e.g., Hawkes process) have been studied extensively yet separately for the two types of correlations in the past. In this paper, we propose a Bayesian nonparametric approach that considers both types of correlations via unifying and generalizing the hidden semiMarkov model and interaction point process model. The proposed approach can simultaneously model both the observations and arrival times of temporal events, and automatically determine the number of latent states from data.

Do any bugs live in the ocean? Crustaceans and insects share a common ancestor, but bugs are happier on land. Water striders are the only insect that live entirely on the ocean's surface. Breakthroughs, discoveries, and DIY tips sent six days a week. By some estimates, insects make up 80 percent of named animal species.