3,125 research outputs found
Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines
Solving nesting problems or irregular strip packing problems is to position
polygons in a fixed width and unlimited length strip, obeying polygon integrity
containment constraints and non-overlapping constraints, in order to minimize
the used length of the strip. To ensure non-overlapping, we used separation
lines. A straight line is a separation line if given two polygons, all vertices
of one of the polygons are on one side of the line or on the line, and all
vertices of the other polygon are on the other side of the line or on the line.
Since we are considering free rotations of the polygons and separation lines,
the mathematical model of the studied problem is nonlinear. Therefore, we use
the nonlinear programming solver IPOPT (an algorithm of interior points type),
which is part of COIN-OR. Computational tests were run using established
benchmark instances and the results were compared with the ones obtained with
other methodologies in the literature that use free rotation
Decentralization Estimators for Instrumental Variable Quantile Regression Models
The instrumental variable quantile regression (IVQR) model (Chernozhukov and
Hansen, 2005) is a popular tool for estimating causal quantile effects with
endogenous covariates. However, estimation is complicated by the non-smoothness
and non-convexity of the IVQR GMM objective function. This paper shows that the
IVQR estimation problem can be decomposed into a set of conventional quantile
regression sub-problems which are convex and can be solved efficiently. This
reformulation leads to new identification results and to fast, easy to
implement, and tuning-free estimators that do not require the availability of
high-level "black box" optimization routines
Learning and Interpreting Multi-Multi-Instance Learning Networks
We introduce an extension of the multi-instance learning problem where
examples are organized as nested bags of instances (e.g., a document could be
represented as a bag of sentences, which in turn are bags of words). This
framework can be useful in various scenarios, such as text and image
classification, but also supervised learning over graphs. As a further
advantage, multi-multi instance learning enables a particular way of
interpreting predictions and the decision function. Our approach is based on a
special neural network layer, called bag-layer, whose units aggregate bags of
inputs of arbitrary size. We prove theoretically that the associated class of
functions contains all Boolean functions over sets of sets of instances and we
provide empirical evidence that functions of this kind can be actually learned
on semi-synthetic datasets. We finally present experiments on text
classification, on citation graphs, and social graph data, which show that our
model obtains competitive results with respect to accuracy when compared to
other approaches such as convolutional networks on graphs, while at the same
time it supports a general approach to interpret the learnt model, as well as
explain individual predictions.Comment: JML
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