10,817 research outputs found
A Consistent Regularization Approach for Structured Prediction
We propose and analyze a regularization approach for structured prediction
problems. We characterize a large class of loss functions that allows to
naturally embed structured outputs in a linear space. We exploit this fact to
design learning algorithms using a surrogate loss approach and regularization
techniques. We prove universal consistency and finite sample bounds
characterizing the generalization properties of the proposed methods.
Experimental results are provided to demonstrate the practical usefulness of
the proposed approach.Comment: 39 pages, 2 Tables, 1 Figur
Leveraging Low-Rank Relations Between Surrogate Tasks in Structured Prediction
We study the interplay between surrogate methods for structured prediction
and techniques from multitask learning designed to leverage relationships
between surrogate outputs. We propose an efficient algorithm based on trace
norm regularization which, differently from previous methods, does not require
explicit knowledge of the coding/decoding functions of the surrogate framework.
As a result, our algorithm can be applied to the broad class of problems in
which the surrogate space is large or even infinite dimensional. We study
excess risk bounds for trace norm regularized structured prediction, implying
the consistency and learning rates for our estimator. We also identify relevant
regimes in which our approach can enjoy better generalization performance than
previous methods. Numerical experiments on ranking problems indicate that
enforcing low-rank relations among surrogate outputs may indeed provide a
significant advantage in practice.Comment: 42 pages, 1 tabl
A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package
The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.Multi-criteria decision aiding; Multi-attribute utility theory; Choquet integral; Free software
Centrality measures for graphons: Accounting for uncertainty in networks
As relational datasets modeled as graphs keep increasing in size and their
data-acquisition is permeated by uncertainty, graph-based analysis techniques
can become computationally and conceptually challenging. In particular, node
centrality measures rely on the assumption that the graph is perfectly known --
a premise not necessarily fulfilled for large, uncertain networks. Accordingly,
centrality measures may fail to faithfully extract the importance of nodes in
the presence of uncertainty. To mitigate these problems, we suggest a
statistical approach based on graphon theory: we introduce formal definitions
of centrality measures for graphons and establish their connections to
classical graph centrality measures. A key advantage of this approach is that
centrality measures defined at the modeling level of graphons are inherently
robust to stochastic variations of specific graph realizations. Using the
theory of linear integral operators, we define degree, eigenvector, Katz and
PageRank centrality functions for graphons and establish concentration
inequalities demonstrating that graphon centrality functions arise naturally as
limits of their counterparts defined on sequences of graphs of increasing size.
The same concentration inequalities also provide high-probability bounds
between the graphon centrality functions and the centrality measures on any
sampled graph, thereby establishing a measure of uncertainty of the measured
centrality score. The same concentration inequalities also provide
high-probability bounds between the graphon centrality functions and the
centrality measures on any sampled graph, thereby establishing a measure of
uncertainty of the measured centrality score.Comment: Authors ordered alphabetically, all authors contributed equally. 21
pages, 7 figure
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