82,588 research outputs found
Visualizing Deep Networks by Optimizing with Integrated Gradients
Understanding and interpreting the decisions made by deep learning models is
valuable in many domains. In computer vision, computing heatmaps from a deep
network is a popular approach for visualizing and understanding deep networks.
However, heatmaps that do not correlate with the network may mislead human,
hence the performance of heatmaps in providing a faithful explanation to the
underlying deep network is crucial. In this paper, we propose I-GOS, which
optimizes for a heatmap so that the classification scores on the masked image
would maximally decrease. The main novelty of the approach is to compute
descent directions based on the integrated gradients instead of the normal
gradient, which avoids local optima and speeds up convergence. Compared with
previous approaches, our method can flexibly compute heatmaps at any resolution
for different user needs. Extensive experiments on several benchmark datasets
show that the heatmaps produced by our approach are more correlated with the
decision of the underlying deep network, in comparison with other
state-of-the-art approaches
Sketch-based Randomized Algorithms for Dynamic Graph Regression
A well-known problem in data science and machine learning is {\em linear
regression}, which is recently extended to dynamic graphs. Existing exact
algorithms for updating the solution of dynamic graph regression problem
require at least a linear time (in terms of : the size of the graph).
However, this time complexity might be intractable in practice. In the current
paper, we utilize {\em subsampled randomized Hadamard transform} and
\textsf{CountSketch} to propose the first randomized algorithms. Suppose that
we are given an matrix embedding of the graph, where .
Let be the number of samples required for a guaranteed approximation error,
which is a sublinear function of . Our first algorithm reduces time
complexity of pre-processing to .
Then after an edge insertion or an edge deletion, it updates the approximate
solution in time. Our second algorithm reduces time complexity of
pre-processing to , where is the number of nonzero elements of . Then after
an edge insertion or an edge deletion or a node insertion or a node deletion,
it updates the approximate solution in time, with
. Finally, we show
that under some assumptions, if our first algorithm
outperforms our second algorithm and if our second
algorithm outperforms our first algorithm
Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions
We describe the implementation of algorithms to construct and maintain
three-dimensional dynamic Delaunay triangulations with kinetic vertices using a
three-simplex data structure. The code is capable of constructing the geometric
dual, the Voronoi or Dirichlet tessellation. Initially, a given list of points
is triangulated. Time evolution of the triangulation is not only governed by
kinetic vertices but also by a changing number of vertices. We use
three-dimensional simplex flip algorithms, a stochastic visibility walk
algorithm for point location and in addition, we propose a new simple method of
deleting vertices from an existing three-dimensional Delaunay triangulation
while maintaining the Delaunay property. The dual Dirichlet tessellation can be
used to solve differential equations on an irregular grid, to define partitions
in cell tissue simulations, for collision detection etc.Comment: 29 pg (preprint), 12 figures, 1 table Title changed (mainly
nomenclature), referee suggestions included, typos corrected, bibliography
update
Fundamental Bounds and Approaches to Sequence Reconstruction from Nanopore Sequencers
Nanopore sequencers are emerging as promising new platforms for
high-throughput sequencing. As with other technologies, sequencer errors pose a
major challenge for their effective use. In this paper, we present a novel
information theoretic analysis of the impact of insertion-deletion (indel)
errors in nanopore sequencers. In particular, we consider the following
problems: (i) for given indel error characteristics and rate, what is the
probability of accurate reconstruction as a function of sequence length; (ii)
what is the number of `typical' sequences within the distortion bound induced
by indel errors; (iii) using replicated extrusion (the process of passing a DNA
strand through the nanopore), what is the number of replicas needed to reduce
the distortion bound so that only one typical sequence exists within the
distortion bound.
Our results provide a number of important insights: (i) the maximum length of
a sequence that can be accurately reconstructed in the presence of indel and
substitution errors is relatively small; (ii) the number of typical sequences
within the distortion bound is large; and (iii) replicated extrusion is an
effective technique for unique reconstruction. In particular, we show that the
number of replicas is a slow function (logarithmic) of sequence length --
implying that through replicated extrusion, we can sequence large reads using
nanopore sequencers. Our model considers indel and substitution errors
separately. In this sense, it can be viewed as providing (tight) bounds on
reconstruction lengths and repetitions for accurate reconstruction when the two
error modes are considered in a single model.Comment: 12 pages, 5 figure
Graph-Controlled Insertion-Deletion Systems
In this article, we consider the operations of insertion and deletion working
in a graph-controlled manner. We show that like in the case of context-free
productions, the computational power is strictly increased when using a control
graph: computational completeness can be obtained by systems with insertion or
deletion rules involving at most two symbols in a contextual or in a
context-free manner and with the control graph having only four nodes.Comment: In Proceedings DCFS 2010, arXiv:1008.127
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