755 research outputs found
Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Networks
The core operation of current Graph Neural Networks (GNNs) is the aggregation
enabled by the graph Laplacian or message passing, which filters the
neighborhood node information. Though effective for various tasks, in this
paper, we show that they are potentially a problematic factor underlying all
GNN methods for learning on certain datasets, as they force the node
representations similar, making the nodes gradually lose their identity and
become indistinguishable. Hence, we augment the aggregation operations with
their dual, i.e. diversification operators that make the node more distinct and
preserve the identity. Such augmentation replaces the aggregation with a
two-channel filtering process that, in theory, is beneficial for enriching the
node representations. In practice, the proposed two-channel filters can be
easily patched on existing GNN methods with diverse training strategies,
including spectral and spatial (message passing) methods. In the experiments,
we observe desired characteristics of the models and significant performance
boost upon the baselines on 9 node classification tasks
Differentiable Genetic Programming for High-dimensional Symbolic Regression
Symbolic regression (SR) is the process of discovering hidden relationships
from data with mathematical expressions, which is considered an effective way
to reach interpretable machine learning (ML). Genetic programming (GP) has been
the dominator in solving SR problems. However, as the scale of SR problems
increases, GP often poorly demonstrates and cannot effectively address the
real-world high-dimensional problems. This limitation is mainly caused by the
stochastic evolutionary nature of traditional GP in constructing the trees. In
this paper, we propose a differentiable approach named DGP to construct GP
trees towards high-dimensional SR for the first time. Specifically, a new data
structure called differentiable symbolic tree is proposed to relax the discrete
structure to be continuous, thus a gradient-based optimizer can be presented
for the efficient optimization. In addition, a sampling method is proposed to
eliminate the discrepancy caused by the above relaxation for valid symbolic
expressions. Furthermore, a diversification mechanism is introduced to promote
the optimizer escaping from local optima for globally better solutions. With
these designs, the proposed DGP method can efficiently search for the GP trees
with higher performance, thus being capable of dealing with high-dimensional
SR. To demonstrate the effectiveness of DGP, we conducted various experiments
against the state of the arts based on both GP and deep neural networks. The
experiment results reveal that DGP can outperform these chosen peer competitors
on high-dimensional regression benchmarks with dimensions varying from tens to
thousands. In addition, on the synthetic SR problems, the proposed DGP method
can also achieve the best recovery rate even with different noisy levels. It is
believed this work can facilitate SR being a powerful alternative to
interpretable ML for a broader range of real-world problems
Using Q methodology to investigate pre-service EFL teachers’ mindsets about teaching competences
This paper reports on a study investigating the mindsets of 51 pre-service teachers at an Austrian university using Q methodology. Despite the recent growth in interest in the concept of mindsets, little research has addressed the mindsets of teachers – most of it focusing on the mindsets of learners – and the research that does investigate teachers tends to focus on beliefs about learning or intelligence. This study offers a new perspective by focusing on teachers’ beliefs about their own teaching competences. A further aim of the study is to expand the methodological repertoire in language education researchers. This study considers the potential of Q methodology, a research approach used widely in social sciences and education, but, as yet, rare in this field. The data indicate that the most common mindset among the pre-service teachers is one based around a strong belief in the learnability of the more technical aspects of teaching, while interpersonal skills tend to be regarded as more of a natural talent fixed within the individual. One practical implication of this finding is that teacher education programmes may need to pay more attention to explicitly developing the interpersonal side of teaching. A further finding was that teacher mindsets are constructed through individuals’ management of various sets of implicit theories and tend not to conform to the established dichotomous model of mindsets.
Robustifying learnability
In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. In addition, we study the cost, in terms of performance in the steady state of a central bank that acts to robustify learnability on the transition path to REE. (Note: This paper contains full-color graphics) JEL Classification: C6, E5E-stability, learnability, Learning, monetary policy, robust control
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