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We study learning outcome prediction for online courses. Whereas prior work has focused on semester-long courses with frequent student assessments, we focus on short-courses that have single outcomes assigned by instructors at the end. The lack of performance data and generally small enrollments makes the behavior of learners, captured as they interact with course content and with one another in Social Learning Networks (SLN), essential for prediction. Our method defines several (machine) learning features based on the processing of behaviors collected on the modes of (human) learning in a course, and uses them in appropriate classifiers. Through evaluation on data captured from three two-week courses hosted through our delivery platforms, we make three key observations: (i) behavioral data contains signals predictive of learning outcomes in short-courses (with classifiers achieving AUCs = 0.8 after the two weeks), (ii) early detection is possible within the first week (AUCs = 0.7 with the first week of data), and (iii) the content features have an "earliest" detection capability (with higher AUC in the first few days), while the SLN features become the more predictive set over time as the network matures. We also discuss how our method can generate behavioral analytics for instructors.

We present the design, implementation, and preliminary evaluation of our Adaptive Educational System (AES): the Mobile Integrated and Individualized Course (MIIC). MIIC is a platform for personalized course delivery which integrates lecture videos, text, assessments, and social learning into a mobile native app, and collects clickstream-level behavioral measurements about each student as they interact with the material. These measurements can subsequently be used to update the student's user model, which can in turn be used to determine the content adaptation. Recruiting students from one of our Massive Open Online Courses (MOOCs), we have conducted two preliminary trials with MIIC, in which we found (i) that the majority of students (70 percent) preferred MIIC overall to a one-size-fits-all (OSFA) presentation of the same material; (ii) that the mean level of engagement, when quantified as the number of pages viewed, was statistically higher (by 72 percent) among students using MIIC than among OSFA; and (iii) that the integrated multimedia learning features were generally favorable among the students (e.g., 87 percent found the videos helpful).

We study user behavior in the courses offered by a major massive online open course (MOOC) provider during the summer of 2013. Since social learning is a key element of scalable education on MOOC and is done via online discussion forums, our main focus is on understanding forum activities. Two salient features of these activities drive our research: (1) high decline rate: for each course studied, the volume of discussion declined continuously throughout the duration of the course; (2) high-volume, noisy discussions: at least 30 percent of the courses produced new threads at rates that are infeasible for students or teaching staff to read through. Further, a substantial portion of these discussions are not directly course-related. In our analysis, we investigate factors that are associated with the decline of activity on MOOC forums, and we find effective strategies to classify threads and rank their relevance. Specifically, we first use linear regression models to analyze the forum activity count data over time, and make a number of observations; for instance, the teaching staff's active participation in the discussions is correlated with an increase in the discussion volume but does not slow down the decline rate. We then propose a unified generative model for the discussion threads, which allows us both to choose efficient thread classifiers and to design an effective algorithm for ranking thread relevance. Further, our algorithm is compared against two baselines using human evaluation from Amazon Mechanical Turk.

Networks need to accommodate diverse applications with different Quality-of-Service (QoS) requirements. New ideas at the physical layer are being developed for this purpose, such as diversity embedded coding, which is a technique that combines high rates with high reliability. We address the problem of how to fully utilize different rate-reliability characteristics at the physical layer to support different types of traffic over a network and to jointly maximize their utilities. We set up a new framework based on utility maximization for networks with composite links, meaning that each link consists of sub-links that can attain different rate-reliability characteristics simultaneously. We incorporate delay, in addition to rate and reliability, into the utility functions. To accommodate different types of traffic, we propose distributed algorithms converging to the optimal rate-reliability-delay tradeoff based on capacity division and priority queueing. Numerical results show that compared with traditional codes, the new codes can provide higher network utilities for all traffic types simultaneously. The results also show that priority queueing achieves higher network utility than capacity division. Index Terms--Networks, resource management, optimization methods, communication systems, channel coding.

Multi-user video streaming over wireless channels is a challenging problem, where the demand for better video quality and small transmission delays needs to be reconciled with the limited and often time-varying communication resources. This paper presents a framework for joint network optimization, source adaptation, and deadline-driven scheduling for multi-user video streaming over wireless networks. We develop a joint adaptation, resource allocation and scheduling (JARS) algorithm, which allocates the communication resource based on the video users' quality of service, adapts video sources based on smart summarization, and schedules the transmissions to meet the frame delivery deadlines. The proposed algorithm leads to near full utilization of the network resources and satisfies the delivery deadlines for all video frames. Substantial performance improvements are achieved compared with heuristic schemes that do not take the interactions between multiple users into consideration. Index Terms--Collaborative video streaming, optimization decomposition, pricing control, rate-distortion modeling, video adaptation.

The implementation of distributed network utility maximization (NUM) algorithms hinges heavily on information feedback through message passing among network elements. In practical systems the feedback is often obtained using error-prone measurement mechanisms and suffers from random errors. In this paper, we investigate the impact of noisy feedback on distributed NUM. We first study the distributed NUM algorithms based on the Lagrangian dual method, and focus on the primal-dual (P-D) algorithm, which is a single time-scale algorithm in the sense that the primal and dual parameters are updated simultaneously. Assuming strong duality, we study both cases when the stochastic gradients are unbiased or biased, and develop a general theory on the stochastic stability of the P-D algorithms in the presence of noisy feedback. When the gradient estimators are unbiased, we establish, via a combination of tools in Martingale theory and convex analysis, that the iterates generated by distributed P-D algorithms converge with probability one to the optimal point, under standard technical conditions. In contrast, when the gradient estimators are biased, we show that the iterates converge to a contraction region around the optimal point, provided that the biased terms are asymptotically bounded by a scaled version of the true gradients. We also investigate the rate of convergence for the unbiased case, and find that, in general, the limit process of the interpolated process corresponding to the normalized iterate sequence is a stationary reflected linear diffusion process, not necessarily a Gaussian diffusion process. We apply the above general theory to investigate stability of cross-layer rate control for joint congestion control and random access. Next, we study the impact of noisy feedback on distributed two time-scale NUM algorithms based on primal decomposition. We establish, via the mean ODE method, the convergence of the stochastic two time-scale algorithm under mild conditions, for the cases where the gradient estimators in both time scales are unbiased. Numerical examples are used to illustrate the finding that compared to the single time-scale counterpart, the two time-scale algorithm, although having lower complexity, is less robust to noisy feedback. Index Terms--Multihop wireless networks, network utility maximization, noisy feedback, primal-dual algorithm, stochastic approximation, stochastic networks, two time-scale algorithm.

Network utility maximization (NUM) problem formulations provide an important approach to conduct network resource allocation and to view layering as optimization decomposition. In the existing literature, distributed implementations are typically achieved by means of the so-called dual decomposition technique. However, the span of decomposition possibilities includes many other elements that, thus far, have not been fully exploited, such as the use of the primal decomposition technique, the versatile introduction of auxiliary variables, and the potential of multilevel decompositions. This paper presents a systematic framework to exploit alternative decomposition structures as a way to obtain different distributed algorithms, each with a different tradeoff among convergence speed, message passing amount and asymmetry, and distributed computation architecture. Several specific applications are considered to illustrate the proposed framework, including resource-constrained and direct-control rate allocation, and rate allocation among QoS classes with multipath routing. For each of these applications, the associated generalized NUM formulation is first presented, followed by the development of novel alternative decompositions and numerical experiments on the resulting new distributed algorithms. A systematic enumeration and comparison of alternative vertical decompositions in the future will help complete a mathematical theory of network architectures. Index Terms--Congestion control, distributed algorithm, mathematical programming/optimization, network control by pricing, network utility maximization (NUM), rate control, resource allocation.

We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E[parallel][S.sup.n] - [[bar.S].sup.n][parallel] for a state-dependent additive Gaussian channel [Y.sup.n] = [X.sup.n] + [S.sup.n] + [Z.sup.n] with an independent and identically distributed (i.i.d.) Gaussian state sequence [S.sup.n] = ([S.sub.1], ..., [S.sub.n]) known at the transmitter and an unknown i.i.d, additive Gaussian noise [Z.sup.]. We show that a simple technique of direct state amplification (i.e., [X.sup.n] = [alpha][S.sup.n]), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification. Index Terms--Additive Gaussian noise channels, channels with state information, joint source-channel coding, state amplification, state estimation.

We show that the Lagrange dual problems of the channel capacity problem with input cost and the rate distortion problem are simple geometric programs. Upper bounds on channel capacity and lower bounds on rate distortion can be efficiently generated from their duals. For channel capacity, the geometric programming dual characterization is shown to be equivalent to the minmax Kullback-Leibler (KL) characterization in [10], [14]. For rate distortion, the geometric programming dual is extended to rate distortion with two-sided state information. A "duality by mapping" is then given between the Lagrange dual problems of channel capacity with input cost and rate distortion, which resolves several apparent asymmetries between their primal problems in the familiar form of mutual information optimization problems. Both the primal and dual problems can be interpreted in a common framework of free energy optimization from statistical physics. Index Terms--Channel capacity, convex optimization, duality, free energy, geometric programming, rate distortion.

The problem of choosing the optimal multipath components to be employed at a minimum mean square error (MMSE) selective Rake receiver is considered for an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an integer programming problem with a nonconvex objective function. Then, the objective function is approximated by a convex function and the integer programming problem is solved by means of constraint relaxation techniques. The proposed algorithms are suboptimal due to the approximate objective function and the constraint relaxation steps. However, they perform better than the conventional finger selection algorithm, which is suboptimal since it ignores the correlation between multipath components, and they can get quite close to the optimal scheme that cannot be implemented in practice due to its complexity. In addition to the convex relaxation techniques, a genetic-algorithm- (GA-) based approach is proposed, which does not need any approximations or integer relaxations. This iterative algorithm is based on the direct evaluation of the objective function, and can achieve near-optimal performance with a reasonable number of iterations. Simulation results are presented to compare the performance of the proposed finger selection algorithms with that of the conventional and the optimal schemes.

Machine learning (ML) tasks are becoming ubiquitous in today's network applications. Federated learning has emerged recently as a technique for training ML models at the network edge by leveraging processing capabilities across the nodes that collect the data. There are several challenges with employing conventional federated learning in contemporary networks, due to the significant heterogeneity in compute and communication capabilities that exist across devices. To address this, we advocate a new learning paradigm called fog learning, which will intelligently distribute ML model training across the continuum of nodes from edge devices to cloud servers. Fog learning enhances federated learning along three major dimensions: network, heterogeneity, and proximity. It considers a multi-layer hybrid learning framework consisting of heterogeneous devices with various proximities. It accounts for the topology structures of the local networks among the heterogeneous nodes at each network layer, orchestrating them for collaborative/cooperative learning through device-to-device communications. This migrates from star network topologies used for parameter transfers in federated learning to more distributed topologies at scale. We discuss several open research directions toward realizing fog learning. [ABSTRACT FROM AUTHOR]

The growing demand for mobile data and the evolution of next-generation networks, particularly fifth-generation (5G) wireless networks, has called for new approaches to pricing and managing the limited capacity of existing network resources and infrastructures. In particular, emerging mobile applications like autonomous vehicles, augmented/virtual reality, and more broadly the Internet-of-Things will have heterogeneous demand patterns and service requirements, raising questions on how they should pay for their data usage and how next-generation networks can meet their demands with limited resources. Several recent policy changes and regulatory initiatives have been proposed to address the shift in demands due to next-generation networks and technologies. These include the FCC’s “5G Fast Plan,” which outlines strategies for modifying spectrum policies, infrastructure policies, and existing regulations, in light of emerging 5G technologies. This plan has included the rollback of net neutrality rules in June 2018, allowing broadband providers to offer a wider variety of service options. [ABSTRACT FROM AUTHOR]

3.1 Information Theory Materials in this subsection are in part based on recent publications [30, 33, 82, 84], and some problems have been studied in the 1980s and 1990s [120, [...]

2.1 Formulations 2.1.1 Basic formulations and convexity property There are two equivalent forms of GP: standard form and convex form. The first is a constrained optimization of a type of [...]

The last section summarizes GP's applications to information theory and queuing theory, coding and signal processing, network resource allocation and protocols. This section initiates an exploration of the plausible reasons [...]

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B.1 Proof of Theorem 3.1 Proof. In order to find the Lagrange dual of problem (3.2), we first form the Lagrangian L as L(p, q, υ, μ, λ, γ) = [...]

In 1961, Zener published a seminal paper [132] in the Proceedings of the National Academy of Sciences, and observed that some engineering design problems can be formulated as optimization of [...]

I would like to acknowledge, first and foremost, Stephen Boyd, who introduced convex optimization to me, and my other co-authors on GP-related publications and preprints: David Julian, Daniel O'Neill, and [...]

1.1 Geometric Programming and Applications Geometric Programming (GP) is a class of nonlinear optimization with many useful theoretical and computational properties. Although GP in standard form is apparently a non-convex [...]

Abstract Geometric Programming (GP) is a class of nonlinear optimization with many useful theoretical and computational properties. Over the last few years, GP has been used to solve a variety [...]