5,969 research outputs found
Learning with Algebraic Invariances, and the Invariant Kernel Trick
When solving data analysis problems it is important to integrate prior
knowledge and/or structural invariances. This paper contributes by a novel
framework for incorporating algebraic invariance structure into kernels. In
particular, we show that algebraic properties such as sign symmetries in data,
phase independence, scaling etc. can be included easily by essentially
performing the kernel trick twice. We demonstrate the usefulness of our theory
in simulations on selected applications such as sign-invariant spectral
clustering and underdetermined ICA
Structure and dynamics in glass-formers: predictability at large length scales
Dynamic heterogeneity in glass-formers has been related to their static
structure using the concept of dynamic propensity. We re-examine this
relationship by analyzing dynamical fluctuations in two atomistic glass-formers
and two theoretical models. We introduce quantitative statistical indicators
which show that the dynamics of individual particles cannot be predicted on the
basis of the propensity, nor by any structural indicator. However, the spatial
structure of the propensity field does have predictive power for the spatial
correlations associated with dynamic heterogeneity. Our results suggest that
the quest for a connection between static and dynamic properties of
glass-formers at the particle level is vain, but they demonstrate that such
connection does exist on larger length scales.Comment: 7 pages; 4 figs - Extended, clarified versio
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Im Rhein, im heiligen Strome (c1860)
Robert Franz
Im Rhein, im heiligen Strome (c1860)
text by Heinrich Heine, Poem 11 of Lyrisches Intermezzo (Buch der Lieder
Bayesian Learning of Sum-Product Networks
Sum-product networks (SPNs) are flexible density estimators and have received
significant attention due to their attractive inference properties. While
parameter learning in SPNs is well developed, structure learning leaves
something to be desired: Even though there is a plethora of SPN structure
learners, most of them are somewhat ad-hoc and based on intuition rather than a
clear learning principle. In this paper, we introduce a well-principled
Bayesian framework for SPN structure learning. First, we decompose the problem
into i) laying out a computational graph, and ii) learning the so-called scope
function over the graph. The first is rather unproblematic and akin to neural
network architecture validation. The second represents the effective structure
of the SPN and needs to respect the usual structural constraints in SPN, i.e.
completeness and decomposability. While representing and learning the scope
function is somewhat involved in general, in this paper, we propose a natural
parametrisation for an important and widely used special case of SPNs. These
structural parameters are incorporated into a Bayesian model, such that
simultaneous structure and parameter learning is cast into monolithic Bayesian
posterior inference. In various experiments, our Bayesian SPNs often improve
test likelihoods over greedy SPN learners. Further, since the Bayesian
framework protects against overfitting, we can evaluate hyper-parameters
directly on the Bayesian model score, waiving the need for a separate
validation set, which is especially beneficial in low data regimes. Bayesian
SPNs can be applied to heterogeneous domains and can easily be extended to
nonparametric formulations. Moreover, our Bayesian approach is the first, which
consistently and robustly learns SPN structures under missing data.Comment: NeurIPS 2019; See conference page for supplemen
Corn stover densification using an auger compactor
Biomass densification is a necessary process for the bio-energy industry. Densities of 224 - 256.3 kg/m3 are needed to minimize transportation costs. Experiments on corn stover densification were completed using an auger compactor. The compaction pressure in the collection tube was varied to establish the pressure\u27s relationship with density and specific energy. Constrained densities of 171 - 343 kg/m3 and unconstrained densities of 131 - 235 kg/m3 were achieved using the system. A power relationship was established between the compaction pressure and the density. A liner relationship was established between the compaction pressure and the specific energy. The minimum bulk densities to optimize transportation fall within the attainable ranges and require less energy than high density processes such as pelletizing and briquetting. Auger compaction appears to be a promising low energy technology for commercial production of densified biomass
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