45,082 research outputs found
Cache Hierarchy Inspired Compression: a Novel Architecture for Data Streams
We present an architecture for data streams based on structures typically found in web cache hierarchies. The main idea is to build a meta level analyser from a number of levels constructed over time from a data stream. We present the general architecture for such a system and an application to classification. This architecture is an instance of the general wrapper idea allowing us to reuse standard batch learning algorithms in an inherently incremental learning environment. By artificially generating data sources we demonstrate that a hierarchy containing a mixture of models is able to adapt over time to the source of the data. In these experiments the hierarchies use an elementary performance based replacement policy and unweighted voting for making classification decisions
Private Incremental Regression
Data is continuously generated by modern data sources, and a recent challenge
in machine learning has been to develop techniques that perform well in an
incremental (streaming) setting. In this paper, we investigate the problem of
private machine learning, where as common in practice, the data is not given at
once, but rather arrives incrementally over time.
We introduce the problems of private incremental ERM and private incremental
regression where the general goal is to always maintain a good empirical risk
minimizer for the history observed under differential privacy. Our first
contribution is a generic transformation of private batch ERM mechanisms into
private incremental ERM mechanisms, based on a simple idea of invoking the
private batch ERM procedure at some regular time intervals. We take this
construction as a baseline for comparison. We then provide two mechanisms for
the private incremental regression problem. Our first mechanism is based on
privately constructing a noisy incremental gradient function, which is then
used in a modified projected gradient procedure at every timestep. This
mechanism has an excess empirical risk of , where is the
dimensionality of the data. While from the results of [Bassily et al. 2014]
this bound is tight in the worst-case, we show that certain geometric
properties of the input and constraint set can be used to derive significantly
better results for certain interesting regression problems.Comment: To appear in PODS 201
Simple, compact and robust approximate string dictionary
This paper is concerned with practical implementations of approximate string
dictionaries that allow edit errors. In this problem, we have as input a
dictionary of strings of total length over an alphabet of size
. Given a bound and a pattern of length , a query has to
return all the strings of the dictionary which are at edit distance at most
from , where the edit distance between two strings and is defined as
the minimum-cost sequence of edit operations that transform into . The
cost of a sequence of operations is defined as the sum of the costs of the
operations involved in the sequence. In this paper, we assume that each of
these operations has unit cost and consider only three operations: deletion of
one character, insertion of one character and substitution of a character by
another. We present a practical implementation of the data structure we
recently proposed and which works only for one error. We extend the scheme to
. Our implementation has many desirable properties: it has a very
fast and space-efficient building algorithm. The dictionary data structure is
compact and has fast and robust query time. Finally our data structure is
simple to implement as it only uses basic techniques from the literature,
mainly hashing (linear probing and hash signatures) and succinct data
structures (bitvectors supporting rank queries).Comment: Accepted to a journal (19 pages, 2 figures
A Lower Bound for the Optimization of Finite Sums
This paper presents a lower bound for optimizing a finite sum of
functions, where each function is -smooth and the sum is -strongly
convex. We show that no algorithm can reach an error in minimizing
all functions from this class in fewer than iterations, where is a
surrogate condition number. We then compare this lower bound to upper bounds
for recently developed methods specializing to this setting. When the functions
involved in this sum are not arbitrary, but based on i.i.d. random data, then
we further contrast these complexity results with those for optimal first-order
methods to directly optimize the sum. The conclusion we draw is that a lot of
caution is necessary for an accurate comparison, and identify machine learning
scenarios where the new methods help computationally.Comment: Added an erratum, we are currently working on extending the result to
randomized algorithm
Sketching space
In this paper, we present a sketch modelling system which we call Stilton. The program resembles a desktop VRML browser, allowing a user to navigate a three-dimensional model in a perspective projection, or panoramic photographs, which the program maps onto the scene as a `floor' and `walls'. We place an imaginary two-dimensional drawing plane in front of the user, and any geometric information that user sketches onto this plane may be reconstructed to form solid objects through an optimization process. We show how the system can be used to reconstruct geometry from panoramic images, or to add new objects to an existing model. While panoramic imaging can greatly assist with some aspects of site familiarization and qualitative assessment of a site, without the addition of some foreground geometry they offer only limited utility in a design context. Therefore, we suggest that the system may be of use in `just-in-time' CAD recovery of complex environments, such as shop floors, or construction sites, by recovering objects through sketched overlays, where other methods such as automatic line-retrieval may be impossible. The result of using the system in this manner is the `sketching of space' - sketching out a volume around the user - and once the geometry has been recovered, the designer is free to quickly sketch design ideas into the newly constructed context, or analyze the space around them. Although end-user trials have not, as yet, been undertaken we believe that this implementation may afford a user-interface that is both accessible and robust, and that the rapid growth of pen-computing devices will further stimulate activity in this area
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