We consider a random sparse graph with bounded average degree, in which a subset of vertices has higher connectivity than the background. In particular, the average degree inside this subset of vertices is larger than outside (but still bounded). Given a realization of such graph, we aim at identifying the hidden subset of vertices. This can be regarded as a model for the problem of finding a tightly knitted community in a social network, or a cluster in a relational dataset. In this paper we present two sets of contributions: $(i)$ We use the cavity method from spin glass theory to derive an exact phase diagram for the reconstruction problem. In particular, as the difference in edge probability increases, the problem undergoes two phase transitions, a static phase transition and a dynamic one. $(ii)$ We establish rigorous bounds on the dynamic phase transition and prove that, above a certain threshold, a local algorithm (belief propagation) correctly identify most of the hidden set. Below the same threshold \emph{no local algorithm} can achieve this goal. However, in this regime the subset can be identified by exhaustive search. For small hidden sets and large average degree, the phase transition for local algorithms takes an intriguingly simple form. Local algorithms succeed with high probability for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} > \sqrt{{\rm deg}_{\rm out}/e}$ and fail for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} < \sqrt{{\rm deg}_{\rm out}/e}$ (with ${\rm deg}_{\rm in}$, ${\rm deg}_{\rm out}$ the average degrees inside and outside the community). We argue that spectral algorithms are also ineffective in the latter regime. It is an open problem whether any polynomial time algorithms might succeed for ${\rm deg}_{\rm in} - {\rm deg}_{\rm out} < \sqrt{{\rm deg}_{\rm out}/e}$.

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we address on-line learning with matrix parameters. It is often easy to obtain online algorithm with good generalization performance if you eigendecompose the current parameter matrix in each trial (at a cost of $O(n^3)$ per trial). Ideally we want to avoid the decompositions and spend $O(n^2)$ per trial, i.e. linear time in the size of the matrix data. There is a core trade-off between the running time and the generalization performance, here measured by the regret of the on-line algorithm (total gain of the best off-line predictor minus the total gain of the on-line algorithm). We focus on the key matrix problem of rank $k$ Principal Component Analysis in $\mathbb{R}^n$ where $k \ll n$. There are $O(n^3)$ algorithms that achieve the optimum regret but require eigendecompositions. We develop a simple algorithm that needs $O(kn^2)$ per trial whose regret is off by a small factor of $O(n^{1/4})$. The algorithm is based on the Follow the Perturbed Leader paradigm. It replaces full eigendecompositions at each trial by the problem finding $k$ principal components of the current covariance matrix that is perturbed by Gaussian noise.

This article presents new algorithms for inferring users' activities in a class We also show that visualizing students' plans improves their performance on new problems when compared to an alternative visualization that consists of a step-by-step list of actions. Such tools can plan visualization outperformed those students who provide support for teachers and education were presented with the list of activities for all of researchers in analyzing and assessing students' use these measures. These contributions demonstrate the benefit of Students' interactions with ELEs are complex, as applying novel plan-recognition technologies toward we illustrate using concepts from an ELE for teaching intelligent analysis of students' interactions in openended the basics of chemistry. Students can engage in and flexible software. Such technologies can exploratory activities involving trial and error, such potentially support teachers in their understanding as searching for the right pair of chemicals to combine of student behavior as well as students in their problem in order to achieve a desired reaction. They can solving and lead to advances in automatic recognition repeat activities indefinitely in pursuit of a goal or in other exploratory domains.

In Massively Open Online Courses (MOOCs) TA resources are limited; most MOOCs use peer assessments to grade assignments. Students have to divide up their time between working on their own homework and grading others. If there is no risk of being caught and penalized, students have no reason to spend any time grading others Course staff want to incentivize students to balance their time between course work and peer grading. They may do so by auditing students, ensuring that they perform grading correctly. One would not want students to invest too much time on peer grading, as this would result in poor course performance. We present the first model of strategic auditing in peer grading, modeling the student's choice of effort in response to a grader's audit levels as a Stackelberg game with multiple followers. We demonstrate that computing the equilibrium for this game is computationally hard. We then provide a PTAS in order to compute an approximate solution to the problem of allocating audit levels. However, we show that this allocation does not necessarily maximize social welfare; in fact, there exist settings where course auditor utility is arbitrarily far from optimal under an approximately optimal allocation. To circumvent this issue, we present a natural condition that guarantees that approximately optimal TA allocations guarantee approximately optimal welfare for the course auditors.

Large formal mathematical knowledge bases encode considerable parts of advanced mathematics and exact science, allowing deep semantic computer assistance and verification of complicated theories down to the atomic logical rules. An essential part of automated reasoning over such large theories are methods learning selection of relevant knowledge from the thousands of proofs in the corpora. Such methods in turn rely on efficiently computable features characterizing the highly structured and inter-related mathematical statements.  In this work we (i) propose novel semantic features characterizing the statements in such large semantic knowledge bases, (ii) propose and carry out their efficient implementation using deductive-AI data-structures such as substitution trees and discrimination nets, and (iii) show that they significantly improve the strength of existing knowledge selection methods and automated reasoning methods over the large formal knowledge bases. In particular, on a standard large-theory benchmark we improve the average predicted rank of a mathematical statement needed for a proof by 22% in comparison with state of the art. This allows us to prove 8% more theorems in comparison with state of the art.

Planning is an important AI task that gives rise to many hard problems. In order to come up with efficient algorithms for this setting, it is important to understand the sources of complexity. For planning problems that are beyond NP, identifying fragments that allow an efficient reduction to SAT can be a feasible approach due to the great performance of modern SAT solvers. In this paper, we use the framework of parameterized complexity theory to obtain a more fine-grained complexity analysis of natural planning problems beyond NP. With this analysis we are able to point out several variants of planning where the structure in the input makes encodings into SAT feasible. We complement these positive results with some hardness results and a new machine characterization for the intractability class exists * for all k-W[P] .

Given a class of students, and a pool of questions in the domain of study, what subset will constitute a good exam? Millions of educators are dealing with this difficult problem worldwide, yet exams are still composed manually in non-systematic ways. In this work we present a novel algorithmic framework for exam composition. Our framework requires two input components: a student population represented by a distribution over overlay models, each consisting of a set of mastered abilities, or actions; and a target model ordering that, given any two student models, defines which should be given the higher grade. To determine the performance of a student model on a potential question, we test whether it satisfies a disjunctive action landmark, i.e., whether its abilities are sufficient to follow at least one solution path. We present a novel utility function for evaluating exams, using the described components. An exam is highly evaluated if it is expected to order the student population with high correlation to the target order.The merit of our algorithmic framework is exemplified with real auto-generated questions in the domain of middle-school algebra.

Online multi-task learning is an important capability for lifelong learning agents, enabling them to acquire models for diverse tasks over time and rapidly learn new tasks by building upon prior experience. However, recent progress toward lifelong reinforcement learning (RL) has been limited to learning from within a single task domain. For truly versatile lifelong learning, the agent must be able to autonomously transfer knowledge between different task domains. A few methods for cross-domain transfer have been developed, but these methods are computationally inefficient for scenarios where the agent must learn tasks consecutively. In this paper, we develop the first cross-domain lifelong RL framework. Our approach efficiently optimizes a shared repository of transferable knowledge and learns projection matrices that specialize that knowledge to different task domains. We provide rigorous theoretical guarantees on the stability of this approach, and empirically evaluate its performance on diverse dynamical systems. Our results show that the proposed method can learn effectively from interleaved task domains and rapidly acquire high performance in new domains.

Cognitive modelling can discover the latent characteristics of examinees for predicting their performance (i.e. scores) on each problem. As cognitive modelling is important for numerous applications, e.g. personalized remedy recommendation, some solutions have been designed in the literature. However, the problem of extracting information from both objective and subjective problems to get more precise and interpretable cognitive analysis is still underexplored. To this end, we propose a fuzzy cognitive diagnosis framework (FuzzyCDF) for examinees' cognitive modelling with both objective and subjective problems. Specifically, to handle the partially correct responses on subjective problems, we first fuzzify the skill proficiency of examinees. Then, we combine fuzzy set theory and educational hypotheses to model the examinees' mastery on the problems. Further, we simulate the generation of examination scores by considering both slip and guess factors. Extensive experiments on three real-world datasets prove that FuzzyCDF can predict examinee performance more effectively, and the output of FuzzyCDF is also interpretative.

Parallel Test Paper Generation ( k -TPG) is a biobjective distributed resource allocation problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified criteria.Generating high-quality parallel test papers is challenging due to its NP-hardness in maximizing the collective objective functions.In this paper, we propose a Collective Biobjective Optimization (CBO) algorithm for solving k -TPG. CBO is a multi-step greedy-based approximation algorithm, which exploits the submodular property for biobjective optimization of k -TPG.Experiment results have shown that CBO has drastically outperformed the current techniques in terms of paper quality and runtime efficiency.