24,130 research outputs found
Human-like rule optimization for continuous domains
When using machine learning techniques for data mining purposes one of the main requirements is that the learned rule set is represented in a comprehensible form. Simpler rules are preferred as they are expected to perform better on unseen data. At the same time the rules should be specific enough so that the misclassification rate is kept to a minimum. In this paper we present a rule optimizing technique motivated by the psychological studies of human concept learning. The technique allows for reasoning to happen at both higher levels of abstraction and lower level of detail in order to optimize the rule set. Information stored at the higher level allows for optimizing processes such as rule splitting, merging and deleting, while the information stored at the lower level allows for determining the attribute relevance for a particular rule. The attributes detected as irrelevant can be removed and the ones previously detected as irrelevant can be reintroduced if necessary. The method is evaluated on the rules extracted from publicly available real world datasets using different classifiers, and the results demonstrate the effectiveness of the presented rule optimizing technique
Beyond Binomial and Negative Binomial: Adaptation in Bernoulli Parameter Estimation
Estimating the parameter of a Bernoulli process arises in many applications,
including photon-efficient active imaging where each illumination period is
regarded as a single Bernoulli trial. Motivated by acquisition efficiency when
multiple Bernoulli processes are of interest, we formulate the allocation of
trials under a constraint on the mean as an optimal resource allocation
problem. An oracle-aided trial allocation demonstrates that there can be a
significant advantage from varying the allocation for different processes and
inspires a simple trial allocation gain quantity. Motivated by realizing this
gain without an oracle, we present a trellis-based framework for representing
and optimizing stopping rules. Considering the convenient case of Beta priors,
three implementable stopping rules with similar performances are explored, and
the simplest of these is shown to asymptotically achieve the oracle-aided trial
allocation. These approaches are further extended to estimating functions of a
Bernoulli parameter. In simulations inspired by realistic active imaging
scenarios, we demonstrate significant mean-squared error improvements: up to
4.36 dB for the estimation of p and up to 1.80 dB for the estimation of log p.Comment: 13 pages, 16 figure
Beyond binomial and negative binomial: adaptation in Bernoulli parameter estimation
Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of p and up to 1.86 dB for the estimation of log p.https://arxiv.org/abs/1809.08801https://arxiv.org/abs/1809.08801First author draf
The efficiency of individual optimization in the conditions of competitive growth
The paper aims to discuss statistical properties of the multi-agent based
model of competitive growth. Each of the agents is described by growth (or
decay) rule of its virtual "mass" with the rate affected by the interaction
with other agents. The interaction depends on the strategy vector and mutual
distance between agents and both are subjected to the agent's individual
optimization process. Steady-state simulations yield phase diagrams with the
high and low competition phases (HCP and LCP, respectively) separated by
critical point. Particular focus has been made on the indicators of the
power-law behavior of the mass distributions with respect to the critical
regime. In this regime the study has revealed remarkable anomaly in the
optimization efficiency
Algorithmic and Statistical Perspectives on Large-Scale Data Analysis
In recent years, ideas from statistics and scientific computing have begun to
interact in increasingly sophisticated and fruitful ways with ideas from
computer science and the theory of algorithms to aid in the development of
improved worst-case algorithms that are useful for large-scale scientific and
Internet data analysis problems. In this chapter, I will describe two recent
examples---one having to do with selecting good columns or features from a (DNA
Single Nucleotide Polymorphism) data matrix, and the other having to do with
selecting good clusters or communities from a data graph (representing a social
or information network)---that drew on ideas from both areas and that may serve
as a model for exploiting complementary algorithmic and statistical
perspectives in order to solve applied large-scale data analysis problems.Comment: 33 pages. To appear in Uwe Naumann and Olaf Schenk, editors,
"Combinatorial Scientific Computing," Chapman and Hall/CRC Press, 201
A deep matrix factorization method for learning attribute representations
Semi-Non-negative Matrix Factorization is a technique that learns a
low-dimensional representation of a dataset that lends itself to a clustering
interpretation. It is possible that the mapping between this new representation
and our original data matrix contains rather complex hierarchical information
with implicit lower-level hidden attributes, that classical one level
clustering methodologies can not interpret. In this work we propose a novel
model, Deep Semi-NMF, that is able to learn such hidden representations that
allow themselves to an interpretation of clustering according to different,
unknown attributes of a given dataset. We also present a semi-supervised
version of the algorithm, named Deep WSF, that allows the use of (partial)
prior information for each of the known attributes of a dataset, that allows
the model to be used on datasets with mixed attribute knowledge. Finally, we
show that our models are able to learn low-dimensional representations that are
better suited for clustering, but also classification, outperforming
Semi-Non-negative Matrix Factorization, but also other state-of-the-art
methodologies variants.Comment: Submitted to TPAMI (16-Mar-2015
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