Dropout Model Evaluation in MOOCs

The field of learning analytics needs to adopt a more rigorous approach for predictive model evaluation that matches the complex practice of model-building. In this work, we present a procedure to statistically test hypotheses about model performance which goes beyond the state-of-the-practice in the community to analyze both algorithms and feature extraction methods from raw data. We apply this method to a series of algorithms and feature sets derived from a large sample of Massive Open Online Courses (MOOCs). While a complete comparison of all potential modeling approaches is beyond the scope of this paper, we show that this approach reveals a large gap in dropout prediction performance between forum-, assignment-, and clickstream-based feature extraction methods, where the latter is significantly better than the former two, which are in turn indistinguishable from one another. This work has methodological implications for evaluating predictive or AI-based models of student success, and practical implications for the design and targeting of at-risk student models and interventions

An Inflated Ordered Probit Model of Monetary Policy: Evidence from MPC Voting Data

Even in the face of a continuously changing economic environment, interest rates often remain unadjusted for long periods. When rates are moved, the norm is for a series of small unidirectional discrete basis-point changes. To explain these phenomena we suggest a two-equation system combining a “long-run” equation explaining a binary decision to change or not change the interest-rate, and a “shortrun” one based on a simple monetary policy rule. We account for unobserved heterogeneity in both equations, applying the model to unique unit-record level data on the voting preferences of Bank of England Monetary Policy Committee (MPC) members.Interest rates; voting; discrete data; ordered models; inflated outcomes; monetary policy committee

A Method for Evaluating Manufacturing Change in Engineering Design

Design changes are a frequent occurrence over the life of a product that may be initiated by an update to the product functionality, new customer needs, or generational improvements. The costs associated with these changes are undesirable, and are often times greatly inflated by additional, unanticipated changes that result from change propagating throughout the system. Propagation paths occur when an initiating change to a component necessitates subsequent changes to coupled components, as the change continues to propagate throughout the product architecture. The nature of this change propagation is challenging to characterize and accurately predict. To address this issue, a change prediction method is developed that builds upon current change management strategies. The method is comprised of: (1) a design structure matrix (DSM) to model the relationships and connectivity within a system, (2) coupling index (CI) values (ranging from 0 to 1) that assess the likeliness of a change to one component/feature affecting another, and (3) design for manufacturing (DFM) information to provide an estimate of the cost and impact of a change. The method can either be applied at the component level, or through further decomposition, at the interfacing feature level. Modeling the relationships between interfacing features, as opposed to components, offers a more detailed representation of change, but requires more knowledge of the system that may not be available in the earlier stages of design. When evaluating a propagation path, the coupling index values are multiplied together as the path extends, to produce a decreased probability for higher orders of coupling. The proposed change prediction method is applied on three industry examples: BMW X5 headliner and center console assemblies, and a Ryobi drill assembly. The method is shown to produce viable results that allow for informed decisions during change management. These results show that the objective measures of coupling and manufacturing cost of change are effective approximations. A comparison of the results from the component and feature based methods show that a feature level analysis offers improvements in accuracy, and sensitivity to uncertainty and path representation. Furthermore, the method proves to be a valuable tool during the initial design of a product, as it can be used to identify features, interfaces, and manufacturing types that will lower a product\u27s overall ease of change

An inequality of Kostka numbers and Galois groups of Schubert problems

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, an easy combinatorial injection proves the inequality. For the remaining cases, we use that these Kostka numbers appear in tensor product decompositions of sl_2(C)-modules. Interpreting the tensor product as the action of certain commuting Toeplitz matrices and using a spectral analysis and Fourier series rewrites the inequality as the positivity of an integral. We establish the inequality by estimating this integral.Comment: Extended abstract for FPSAC 201

Nielsen equalizer theory

We extend the Nielsen theory of coincidence sets to equalizer sets, the points where a given set of (more than 2) mappings agree. On manifolds, this theory is interesting only for maps between spaces of different dimension, and our results hold for sets of k maps on compact manifolds from dimension (k-1)n to dimension n. We define the Nielsen equalizer number, which is a lower bound for the minimal number of equalizer points when the maps are changed by homotopies, and is in fact equal to this minimal number when the domain manifold is not a surface. As an application we give some results in Nielsen coincidence theory with positive codimension. This includes a complete computation of the geometric Nielsen number for maps between tori.Comment: + addendum, sync with published versio