4,063 research outputs found
Machine learning: statistical physics based theory and smart industry applications
The increasing computational power and the availability of data have made it possible to train ever-bigger artificial neural networks. These so-called deep neural networks have been used for impressive applications, like advanced driver assistance and support in medical diagnoses. However, various vulnerabilities have been revealed and there are many open questions concerning the workings of neural networks. Theoretical analyses are therefore essential for further progress. One current question is: why is it that networks with Rectified Linear Unit (ReLU) activation seemingly perform better than networks with sigmoidal activation?We contribute to the answer to this question by comparing ReLU networks with sigmoidal networks in diverse theoretical learning scenarios. In contrast to analysing specific datasets, we use a theoretical modelling using methods from statistical physics. They give the typical learning behaviour for chosen model scenarios. We analyse both the learning behaviour on a fixed dataset and on a data stream in the presence of a changing task. The emphasis is on the analysis of the network’s transition to a state wherein specific concepts have been learnt. We find significant benefits of ReLU networks: they exhibit continuous increases of their performance and adapt more quickly to changing tasks.In the second part of the thesis we treat applications of machine learning: we design a quick quality control method for material in a production line and study the relationship with product faults. Furthermore, we introduce a methodology for the interpretable classification of time series data
Complex-valued embeddings of generic proximity data
Proximities are at the heart of almost all machine learning methods. If the
input data are given as numerical vectors of equal lengths, euclidean distance,
or a Hilbertian inner product is frequently used in modeling algorithms. In a
more generic view, objects are compared by a (symmetric) similarity or
dissimilarity measure, which may not obey particular mathematical properties.
This renders many machine learning methods invalid, leading to convergence
problems and the loss of guarantees, like generalization bounds. In many cases,
the preferred dissimilarity measure is not metric, like the earth mover
distance, or the similarity measure may not be a simple inner product in a
Hilbert space but in its generalization a Krein space. If the input data are
non-vectorial, like text sequences, proximity-based learning is used or ngram
embedding techniques can be applied. Standard embeddings lead to the desired
fixed-length vector encoding, but are costly and have substantial limitations
in preserving the original data's full information. As an information
preserving alternative, we propose a complex-valued vector embedding of
proximity data. This allows suitable machine learning algorithms to use these
fixed-length, complex-valued vectors for further processing. The complex-valued
data can serve as an input to complex-valued machine learning algorithms. In
particular, we address supervised learning and use extensions of
prototype-based learning. The proposed approach is evaluated on a variety of
standard benchmarks and shows strong performance compared to traditional
techniques in processing non-metric or non-psd proximity data.Comment: Proximity learning, embedding, complex values, complex-valued
embedding, learning vector quantizatio
Complex-valued embeddings of generic proximity data
Proximities are at the heart of almost all machine learning methods. If the
input data are given as numerical vectors of equal lengths, euclidean distance,
or a Hilbertian inner product is frequently used in modeling algorithms. In a
more generic view, objects are compared by a (symmetric) similarity or
dissimilarity measure, which may not obey particular mathematical properties.
This renders many machine learning methods invalid, leading to convergence
problems and the loss of guarantees, like generalization bounds. In many cases,
the preferred dissimilarity measure is not metric, like the earth mover
distance, or the similarity measure may not be a simple inner product in a
Hilbert space but in its generalization a Krein space. If the input data are
non-vectorial, like text sequences, proximity-based learning is used or ngram
embedding techniques can be applied. Standard embeddings lead to the desired
fixed-length vector encoding, but are costly and have substantial limitations
in preserving the original data's full information. As an information
preserving alternative, we propose a complex-valued vector embedding of
proximity data. This allows suitable machine learning algorithms to use these
fixed-length, complex-valued vectors for further processing. The complex-valued
data can serve as an input to complex-valued machine learning algorithms. In
particular, we address supervised learning and use extensions of
prototype-based learning. The proposed approach is evaluated on a variety of
standard benchmarks and shows strong performance compared to traditional
techniques in processing non-metric or non-psd proximity data.Comment: Proximity learning, embedding, complex values, complex-valued
embedding, learning vector quantizatio
Learning vector quantization and relevances in complex coefficient space
In this contribution, we consider the classification of time series and similar functional data which can be represented in complex Fourier and wavelet coefficient space. We apply versions of learning vector quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger calculus. It allows for the formulation of gradient-based update rules in the framework of cost-function-based generalized matrix relevance LVQ (GMLVQ). Alternatively, we consider the concatenation of real and imaginary parts of Fourier coefficients in a real-valued feature vector and the classification of time-domain representations by means of conventional GMLVQ. In addition, we consider the application of the method in combination with wavelet-space features to heartbeat classification
Regression with Linear Factored Functions
Many applications that use empirically estimated functions face a curse of
dimensionality, because the integrals over most function classes must be
approximated by sampling. This paper introduces a novel regression-algorithm
that learns linear factored functions (LFF). This class of functions has
structural properties that allow to analytically solve certain integrals and to
calculate point-wise products. Applications like belief propagation and
reinforcement learning can exploit these properties to break the curse and
speed up computation. We derive a regularized greedy optimization scheme, that
learns factored basis functions during training. The novel regression algorithm
performs competitively to Gaussian processes on benchmark tasks, and the
learned LFF functions are with 4-9 factored basis functions on average very
compact.Comment: Under review as conference paper at ECML/PKDD 201
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