We consider the problem of Probably Approximate Correct (PAC) learning of a binary classifier from noisy labeled examples acquired from multiple annotators (each characterized by a respective classification noise rate). First, we consider the complete information scenario, where the learner knows the noise rates of all the annotators. For this scenario, we derive sample complexity bound for the Minimum Disagreement Algorithm (MDA) on the number of labeled examples to be obtained from each annotator. Next, we consider the incomplete information scenario, where each annotator is strategic and holds the respective noise rate as a private information. For this scenario, we design a cost optimal procurement auction mechanism along the lines of Myerson's optimal auction design framework in a non-trivial manner. This mechanism satisfies incentive compatibility property, thereby facilitating the learner to elicit true noise rates of all the annotators.

We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our bounds are always tighter and in some cases substantially improve upon previous ones based on the $L_1$ distance. We also present a generalization of the standard on-line to batch conversion to the drifting scenario in terms of the discrepancy and arbitrary convex combinations of hypotheses. We introduce a new algorithm exploiting these learning guarantees, which we show can be formulated as a simple QP. Finally, we report the results of preliminary experiments demonstrating the benefits of this algorithm.

In the supervised learning setting termed Multiple-Instance Learning (MIL), the examples are bags of instances, and the bag label is a function of the labels of its instances. Typically, this function is the Boolean OR. The learner observes a sample of bags and the bag labels, but not the instance labels that determine the bag labels. The learner is then required to emit a classification rule for bags based on the sample. MIL has numerous applications, and many heuristic algorithms have been used successfully on this problem, each adapted to specific settings or applications. In this work we provide a unified theoretical analysis for MIL, which holds for any underlying hypothesis class, regardless of a specific application or problem domain. We show that the sample complexity of MIL is only poly-logarithmically dependent on the size of the bag, for any underlying hypothesis class. In addition, we introduce a new PAC-learning algorithm for MIL, which uses a regular supervised learning algorithm as an oracle. We prove that efficient PAC-learning for MIL can be generated from any efficient non-MIL supervised learning algorithm that handles one-sided error. The computational complexity of the resulting algorithm is only polynomially dependent on the bag size.

Recent developments in reinforcement learning for non-Markovianproblems witness a surge in history-based methods, among which weare particularly interested in two frameworks, PhiMDP and MC-AIXI-CTW. PhiMDP attempts to reduce the general RL problem, where the environment's states and dynamics are both unknown, toan MDP, while MC-AIXI-CTW incrementally learns a mixture of contexttrees as its environment model. The main idea of PhiMDP is toconnect generic reinforcement learning with classical reinforcementlearning. The first implementation of PhiMDP relies on astochastic search procedure for finding a tree that minimizes acertain cost function. This does not guarantee finding theminimizing tree, or even a good one, given limited search time. As aconsequence it appears that the approach has difficulties with largedomains. MC-AIXI-CTW is attractive in that it can incrementally andanalytically compute the internal model through interactions withthe environment. Unfortunately, it is computationally demanding dueto requiring heavy planning simulations at every single time step.We devise a novel approach called CTMRL, which analytically andefficiently finds the cost-minimizing tree. Instead of thecontext-tree weighting method that MC-AIXI-CTW is based on, we usethe closely related context-tree maximizing algorithm that selectsjust one single tree. This approach falls under the PhiMDPframework, which allows the replacement of the costly planningcomponent of MC-AIXI-CTW with simple Q-Learning. Our empiricalinvestigation show that CTMRL finds policies of quality as good as MC-AIXI-CTW's on sixdomains including a challenging Pacman domain, but in an order ofmagnitude less time.

It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same time measurability of the hypotheses is a necessary condition for learnability. In this thesis we discuss when a sample compression scheme, created from com- pression schemes on finite subspaces via the compactness theorem, have measurable hypotheses. We show that if X is a standard Borel space with a d-maximum and universally separable concept class C, then (X,C) has a sample compression scheme of size d with universally Borel measurable hypotheses. Additionally we introduce a new variant of compression scheme called a copy sample compression scheme.

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as well as any oblivious kernel predictor. The paper contains the derivation of an estimate on the performance of this algorithm. The estimate is then used to derive an application of the Complexity Approximation Principle to kernel methods.

Modern SAT solvers are routinely used as core solving engines in vast numbers of different AI and industrial applications. In this short article, we will provide an overview of the SAT solver competitions. The solvers), and another one based on wall clock time, second SAT competition took place during the second which promotes solvers using all available Dimacs challenge in 1993 (Johnson and Trick resources to answer as quickly as possible (for 1996). Another SAT competition took place in answers incorrectly if it reports satisfiable but Beijing in 1996, organized by James Crawford. Each survey propagation (Braunstein and Zecchina category is defined through the type of instances 2004), a new approach to efficiently solve randomly used as benchmarks.

In response to a 1997 problem of M. Vidyasagar, we state a criterion for PAC learnability of a concept class $\mathscr C$ under the family of all non-atomic (diffuse) measures on the domain $\Omega$. The uniform Glivenko--Cantelli property with respect to non-atomic measures is no longer a necessary condition, and consistent learnability cannot in general be expected. Our criterion is stated in terms of a combinatorial parameter $\VC({\mathscr C}\,{\mathrm{mod}}\,\omega_1)$ which we call the VC dimension of $\mathscr C$ modulo countable sets. The new parameter is obtained by "thickening up" single points in the definition of VC dimension to uncountable "clusters". Equivalently, $\VC(\mathscr C\modd\omega_1)\leq d$ if and only if every countable subclass of $\mathscr C$ has VC dimension $\leq d$ outside a countable subset of $\Omega$. The new parameter can be also expressed as the classical VC dimension of $\mathscr C$ calculated on a suitable subset of a compactification of $\Omega$. We do not make any measurability assumptions on $\mathscr C$, assuming instead the validity of Martin's Axiom (MA). Similar results are obtained for function learning in terms of fat-shattering dimension modulo countable sets, but, just like in the classical distribution-free case, the finiteness of this parameter is sufficient but not necessary for PAC learnability under non-atomic measures.

We consider the problem of learning classifiers for labeled data that has been distributed across several nodes. Our goal is to find a single classifier, with small approximation error, across all datasets while minimizing the communication between nodes. This setting models real-world communication bottlenecks in the processing of massive distributed datasets. We present several very general sampling-based solutions as well as some two-way protocols which have a provable exponential speed-up over any one-way protocol. We focus on core problems for noiseless data distributed across two or more nodes. The techniques we introduce are reminiscent of active learning, but rather than actively probing labels, nodes actively communicate with each other, each node simultaneously learning the important data from another node.

Learning theory has largely focused on two main learning scenarios: the classical statistical setting where instances are drawn i.i.d. from a fixed distribution, and the adversarial scenario whereby at every time step the worst instance is revealed to the player. It can be argued that in the real world neither of these assumptions is reasonable. We define the minimax value of a game where the adversary is restricted in his moves, capturing stochastic and non-stochastic assumptions on data. Building on the sequential symmetrization approach, we define a notion of distribution-dependent Rademacher complexity for the spectrum of problems ranging from i.i.d. to worst-case. The bounds let us immediately deduce variation-type bounds. We study a smoothed online learning scenario and show that exponentially small amount of noise can make function classes with infinite Littlestone dimension learnable.