30,778 research outputs found
Understanding and Improving Proximity Graph based Maximum Inner Product Search
The inner-product navigable small world graph (ip-NSW) represents the
state-of-the-art method for approximate maximum inner product search (MIPS) and
it can achieve an order of magnitude speedup over the fastest baseline.
However, to date it is still unclear where its exceptional performance comes
from. In this paper, we show that there is a strong norm bias in the MIPS
problem, which means that the large norm items are very likely to become the
result of MIPS. Then we explain the good performance of ip-NSW as matching the
norm bias of the MIPS problem - large norm items have big in-degrees in the
ip-NSW proximity graph and a walk on the graph spends the majority of
computation on these items, thus effectively avoids unnecessary computation on
small norm items. Furthermore, we propose the ip-NSW+ algorithm, which improves
ip-NSW by introducing an additional angular proximity graph. Search is first
conducted on the angular graph to find the angular neighbors of a query and
then the MIPS neighbors of these angular neighbors are used to initialize the
candidate pool for search on the inner-product proximity graph. Experiment
results show that ip-NSW+ consistently and significantly outperforms ip-NSW and
provides more robust performance under different data distributions.Comment: 8 pages, 8 figure
Distributed PCP Theorems for Hardness of Approximation in P
We present a new distributed model of probabilistically checkable proofs
(PCP). A satisfying assignment to a CNF formula is
shared between two parties, where Alice knows , Bob knows
, and both parties know . The goal is to have
Alice and Bob jointly write a PCP that satisfies , while
exchanging little or no information. Unfortunately, this model as-is does not
allow for nontrivial query complexity. Instead, we focus on a non-deterministic
variant, where the players are helped by Merlin, a third party who knows all of
.
Using our framework, we obtain, for the first time, PCP-like reductions from
the Strong Exponential Time Hypothesis (SETH) to approximation problems in P.
In particular, under SETH we show that there are no truly-subquadratic
approximation algorithms for Bichromatic Maximum Inner Product over
{0,1}-vectors, Bichromatic LCS Closest Pair over permutations, Approximate
Regular Expression Matching, and Diameter in Product Metric. All our
inapproximability factors are nearly-tight. In particular, for the first two
problems we obtain nearly-polynomial factors of ; only
-factor lower bounds (under SETH) were known before
Visualizing and Understanding Sum-Product Networks
Sum-Product Networks (SPNs) are recently introduced deep tractable
probabilistic models by which several kinds of inference queries can be
answered exactly and in a tractable time. Up to now, they have been largely
used as black box density estimators, assessed only by comparing their
likelihood scores only. In this paper we explore and exploit the inner
representations learned by SPNs. We do this with a threefold aim: first we want
to get a better understanding of the inner workings of SPNs; secondly, we seek
additional ways to evaluate one SPN model and compare it against other
probabilistic models, providing diagnostic tools to practitioners; lastly, we
want to empirically evaluate how good and meaningful the extracted
representations are, as in a classic Representation Learning framework. In
order to do so we revise their interpretation as deep neural networks and we
propose to exploit several visualization techniques on their node activations
and network outputs under different types of inference queries. To investigate
these models as feature extractors, we plug some SPNs, learned in a greedy
unsupervised fashion on image datasets, in supervised classification learning
tasks. We extract several embedding types from node activations by filtering
nodes by their type, by their associated feature abstraction level and by their
scope. In a thorough empirical comparison we prove them to be competitive
against those generated from popular feature extractors as Restricted Boltzmann
Machines. Finally, we investigate embeddings generated from random
probabilistic marginal queries as means to compare other tractable
probabilistic models on a common ground, extending our experiments to Mixtures
of Trees.Comment: Machine Learning Journal paper (First Online), 24 page
SoK: Cryptographically Protected Database Search
Protected database search systems cryptographically isolate the roles of
reading from, writing to, and administering the database. This separation
limits unnecessary administrator access and protects data in the case of system
breaches. Since protected search was introduced in 2000, the area has grown
rapidly; systems are offered by academia, start-ups, and established companies.
However, there is no best protected search system or set of techniques.
Design of such systems is a balancing act between security, functionality,
performance, and usability. This challenge is made more difficult by ongoing
database specialization, as some users will want the functionality of SQL,
NoSQL, or NewSQL databases. This database evolution will continue, and the
protected search community should be able to quickly provide functionality
consistent with newly invented databases.
At the same time, the community must accurately and clearly characterize the
tradeoffs between different approaches. To address these challenges, we provide
the following contributions:
1) An identification of the important primitive operations across database
paradigms. We find there are a small number of base operations that can be used
and combined to support a large number of database paradigms.
2) An evaluation of the current state of protected search systems in
implementing these base operations. This evaluation describes the main
approaches and tradeoffs for each base operation. Furthermore, it puts
protected search in the context of unprotected search, identifying key gaps in
functionality.
3) An analysis of attacks against protected search for different base
queries.
4) A roadmap and tools for transforming a protected search system into a
protected database, including an open-source performance evaluation platform
and initial user opinions of protected search.Comment: 20 pages, to appear to IEEE Security and Privac
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