6,322 research outputs found
Practical Bayesian Optimization of Machine Learning Algorithms
Machine learning algorithms frequently require careful tuning of model
hyperparameters, regularization terms, and optimization parameters.
Unfortunately, this tuning is often a "black art" that requires expert
experience, unwritten rules of thumb, or sometimes brute-force search. Much
more appealing is the idea of developing automatic approaches which can
optimize the performance of a given learning algorithm to the task at hand. In
this work, we consider the automatic tuning problem within the framework of
Bayesian optimization, in which a learning algorithm's generalization
performance is modeled as a sample from a Gaussian process (GP). The tractable
posterior distribution induced by the GP leads to efficient use of the
information gathered by previous experiments, enabling optimal choices about
what parameters to try next. Here we show how the effects of the Gaussian
process prior and the associated inference procedure can have a large impact on
the success or failure of Bayesian optimization. We show that thoughtful
choices can lead to results that exceed expert-level performance in tuning
machine learning algorithms. We also describe new algorithms that take into
account the variable cost (duration) of learning experiments and that can
leverage the presence of multiple cores for parallel experimentation. We show
that these proposed algorithms improve on previous automatic procedures and can
reach or surpass human expert-level optimization on a diverse set of
contemporary algorithms including latent Dirichlet allocation, structured SVMs
and convolutional neural networks
Bayesian Optimization with Unknown Constraints
Recent work on Bayesian optimization has shown its effectiveness in global
optimization of difficult black-box objective functions. Many real-world
optimization problems of interest also have constraints which are unknown a
priori. In this paper, we study Bayesian optimization for constrained problems
in the general case that noise may be present in the constraint functions, and
the objective and constraints may be evaluated independently. We provide
motivating practical examples, and present a general framework to solve such
problems. We demonstrate the effectiveness of our approach on optimizing the
performance of online latent Dirichlet allocation subject to topic sparsity
constraints, tuning a neural network given test-time memory constraints, and
optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed
time, subject to passing standard convergence diagnostics.Comment: 14 pages, 3 figure
Observing the Spontaneous Breakdown of Unitarity
During the past decade, the experimental development of being able to create
ever larger and heavier quantum superpositions has brought the discussion of
the connection between microscopic quantum mechanics and macroscopic classical
physics back to the forefront of physical research. Under equilibrium
conditions this connection is in fact well understood in terms of the mechanism
of spontaneous symmetry breaking, while the emergence of classical dynamics can
be described within an ensemble averaged description in terms of decoherence.
The remaining realm of individual-state quantum dynamics in the thermodynamic
limit was addressed in a recent paper proposing that the unitarity of quantum
mechanical time evolution in macroscopic objects may be susceptible to a
spontaneous breakdown. Here we will discuss the implications of this theory of
spontaneous unitarity breaking for the modern experiments involving truly
macroscopic Schrodinger cat states.Comment: 4 pages, no figure
An organic geochemical approach to problems of glacial-interglacial climatic variability
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1988The concentration and carbon isotopic composition (δ13C) of
sedimentary organic carbon (Corg), N/C ratios, and terrigenous and
marine δ13C-Corg end-members form a basis from which to address
problems of Late Quaternary glacial-interglacial climatic variability
in a 208.7 m hydraulic piston core (DSDP 619) from the Pigmy Basin in
the northern Gulf of Mexico. Paired analyses of δ13C-Corg and N/C
are consistent with the hypothesis that the sedimentary organic carbon
in the Pigmy Basin is a climatically-determined mixture of
C3-photosynthetic terrigenous and marine organic matter, confirming
the model of Sackett (1964). A high resolution (~1.4-2.7 ky/sample)
δ13C-Corg record shows that sedimentary organic carbon in
interglacial oxygen isotope (sub)stages 1 and 5a-b are enriched in
13C (average ± 10 values are -24.2 ± 1.2% 0 and -23.0 ±
0.8% relative to PDB, respectively) while glacial isotope stage
values 2 are relatively depleted (-25.6 ± 0.5%).
Concentrations of terrigenous and marine sedimentary organic carbon
are calculated using δ13C-Corg and Corg measurements, and
terrigenous and marine δ13C-Corg end-members. The net
accumulation rate of terrigenous organic carbon is 3.7±3.1 times
higher in isotope stages 2-4 than in (sub)stages 1 and 5a-b, recording
higher erosion rates of terrigenous organic material in glacial
periods than interglacial periods. The concentration and net
accumulation rates of marine and terrigenous Corg suggest that the
nutrient-bearing plume of the Mississippi River may have advanced and
retreated across the Pigmy Basin as sea level fell and rose in
response to glacial-interglacial sea level change.
A study of selected organic biomarker compounds which could
serve as tracers of terrigenous and marine sedimentary organic matter
sources was performed by comparison with contemporaneous sedimentary
organic carbon isotopic composition (δ13C-Corg). Organic
carbon-normalized concentrations of total long chain (C37-C39)
unsaturated alkenones and individual C27-C29 desmethyl sterols
were determined to be useful proportional indicators of preserved
marine and terrigenous organic carbon, respectively. The a1kenones,
whose source is marine phytoplankton of the class Prymnesiophyceae,
generally occurred in higher concentrations in interglacial isotope
stages 1 and 5a-b than in the intervening stages, including glacial
stages 2 and 4. Sterols (C27-C29) of a dominantly terrigenous
origin had lower concentrations during interglacial stages than in
glacial stages. The sedimentary records of both terrigenous and
marine organic carbon-normalized biomarker compound concentrations
appear to be systematically altered by the remineralization of
sedimentary organic carbon, as indicated by a simple, first-order
organic carbon decay model. The sedimentary deposition of some
terrigenous 4-desmethy1stero1s may be affected by differential
hydraulic particle sorting as they are transported from river deltas
across the continental shelf and slope to the hemipelagic Pigmy
Basin. The marine phytoplanktonic alkenones which originate in the
surface ocean and sink through the water column would not be subject
to comparable particle sorting. The lack of any 4-desmethyl- or
4-α-methy1sterol which was linearly related to the proportion of
marine sedimentary organic matter (as scaled by δ13C-Corg)
indicated that either (1) sedimentary diagenesis had obscured the
biomarker/Corg versus δ13C-Corg record, or (2) the selected
compounds were not proportional indicators of preserved marine organic
carbon input.
The diagenetic alteration of the sedimentary sterol concentration
records in which marine sterols were apparently more susceptible to
degradation than terrigenous sterols was consistent with present-day
sediment trap and recent (10-1-102y) sediment core observations.
Preferential preservation of terrigenous sterols may result in a
biased sedimentary record of sterol input which could be
misinterpreted as indicating solely terrigenous sterol sources. The
value and limitations of a simple model which characterizes the
effects of sedimentary diagenesis and source input changes on the
relationship between organic carbon-normalized biomarker compounds and
sedimentary organic matter carbon isotopic composition are discussed.
The potential occurrence of sterol double bond hydrogenations
(Δ5',Δ22) in three classes of C27-29-4-desmethy1stero1s was
evaluated by examining the time series of expected product/precursor
relationships with sterol data from the ~2-100kybp DSDP 619 record.
Only the Δ5-hydrogenations of the C29 sterols (24-ethy1cholest-5-en-
3β-01, 24-ethylcholesta-5,22-dien-3β-01) showed significant
temporally-increasing trends. The 24-ethy1cho1estan-3β-01/24-ethy1cho1est-
5-en-3β-ol (C29Δ°/C29Δ5) ratio also positively
correlated with paired sedimentary organic carbon isotopic composition
(δ13C-Corg) values. This may be due to increased susceptibility
to diagenetic transformation reactions by the organic matter
accompanying finer grain-sized terrigenous sediment particles. A
long-term source change of 24-ethylcholestan-3β-01 relative to
24-ethylcholest-5-en-3β-01 to explain the correlation with
δ13C-Corg seems less likely since both compounds are predominantly
of a terrigenous origin in the Pigmy Basin. A comparison of
histograms of stanol/stenol (ΔO/Δ5) ratios for the C27-29 -4-desmethylsterols
indicates the following sequence in the relative
degree of tranformation: C27 > C28 > C29. The C27 - and C28-sterols appear to have attained their respective degrees of
transformation before -2kybp, perhaps prior to deposition in the Pigmy
Basin. However, differential rates of competing reactions of both the
precursor and products may have obscured these simple transformation
ratio records.
The sedimentary record of a ratio (Uk37) of long chain (C37)
unsaturated alkenones is a useful indicator of glacial-interglacial
climatic change in the Late Quaternary northern Gulf of Mexico where a
planktonic foraminiferal δ18O-CaCO3 record is complicated by
meltwater and/or fluvial events (Williams and Kohl, 1986). Using
laboratory temperature calibration data of the Uk37 ratio (Prahl
and Wakeham, 1987), it is suggested that the minimum glacial surface
mixed layer (SML) temperature was 8±1°C colder than the Holocene high
SML temperature of 25.6±O.5°C in a Pigmy Basin hydraulic piston core
(DSDP 619). However, this glacial-interglacial Uk37-temperature
difference was significantly larger than the differences predicted by
either the foraminiferal δ18O or foraminiferal assemblage
temperature methods (O.8-2.0°C). A possible cause for this large
difference is that the Prymnesiophyte assemblages in this area may
vary in response to climatically-induced hydrographic changes.
Interglacial periods may be dominated by pelagic Prymnesiophyte
assemblages, while glacial periods may be dominated by neritic
assemblages. Correlation of the Uk37 ratio with the sedimentary
organic carbon composition (δ13C-Corg) is consistent with the
predominance of preserved input of erosive terrigenous over marine
organic carbon during glacial stages in the northern Gulf of Mexico
when sea level was as much as 150m lower than in the present
interglacial stage. Marine organic carbon burial dominated in warmer
interglacial stages 1 and 5a-b
Recalibrating the compass: towards effective competition law enforcement on mixed markets
The undertaking, a cornerstone of EU competition law, has consistently been approached as a functional concept. Any entity engaged in economic activity should be considered an undertaking, thereby ensuring consistent application of competition law across competitors. However, current national enforcement practice reveals a departure from the functional approach to the undertaking on mixed markets, where public and private firms compete. Particularly, allegedly anticompetitive behaviour by public entities has evaded competition law scrutiny in the Netherlands, because competition law was found not to apply to these public entities. Drawing on a jointly interpreted string of CJEU cases in competition law and state aid law – which this article coins as the “Compass doctrine” – the Dutch competition authority and courts found that economic activity by public entities is exempt from competition law when connected to the exercise of public power. Analysis of the Compass doctrine cases reveals how a number of case-specific outcomes taken together have allowed for an undermining of the functional approach to the undertaking. It is demonstrated how the sum of the Compass doctrine is larger than its individual parts, which seems to have been unforeseen by the CJEU. This article demonstrates how the Compass doctrine has two adverse consequences: (1) because it undermines the functional approach to the undertaking as the subject of competition law, it impedes effective enforcement; (2) the Compass doctrine enables public firms to behave anticompetitively on mixed markets. The CJEU never anticipated the advent of commercial behaviour by public entities, who with the Compass doctrine in hand can infringe competition law with impunity. Experiences in the Netherlands to this effect should be regarded as a canary in the coal mine for mixed markets across the EU. Therefore, it is incumbent on the CJEU to revisit the Compass doctrine in future cases, which may follow from preliminary references. This article recommends the CJEU to (re)emphasize that once an entity is engaged in economic activity, it can no longer escape competition law scrutiny by being connected to the exercise of public authority. To protect the level playing field on mixed markets, all economic activity should explicitly be subject to EU competition law
Effects of industrial development on rural welfare
Writers and exponents of the decentralization-of-industry theory seem to think that it is the hope of rural people. It is not the purpose or intention of this study to prove that industrial development is desirable or objectionable, but to find out its effects on rural welfare as revealed by data collected in four survey areas. Precaution was taken to be fair in all statements and not to be biased or let preconceived ideas about the problem influence the conclusions drawn
Analysis and Modeling of Polysilicon Critical Dimensions
The objective of the project was to evaluate polysilicon CD etch bias as it was affected by etch time, measurement feature within the exposure field, and the product being measured. Characterization of the trends has generated a summarizing model that uses etch time, measurement feature, and product type as significant factors in determining polysilicon CD etch bias. Etch time was found to be a continuous factor, while measurement site and product type were categorical. Measurement Site A was found to be independent of measurement Site B, independent of Site C, etc., as well as Product 1 was found independent of Product 2. When tested with JMP Statistical software the generated model produced an R-sq Adj. =0.96. A comparison of modeled values with collected data for several different combinations of conditions showed a maximum difference of 6% on a normalized scale
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