5,344 research outputs found
MDL Convergence Speed for Bernoulli Sequences
The Minimum Description Length principle for online sequence
estimation/prediction in a proper learning setup is studied. If the underlying
model class is discrete, then the total expected square loss is a particularly
interesting performance measure: (a) this quantity is finitely bounded,
implying convergence with probability one, and (b) it additionally specifies
the convergence speed. For MDL, in general one can only have loss bounds which
are finite but exponentially larger than those for Bayes mixtures. We show that
this is even the case if the model class contains only Bernoulli distributions.
We derive a new upper bound on the prediction error for countable Bernoulli
classes. This implies a small bound (comparable to the one for Bayes mixtures)
for certain important model classes. We discuss the application to Machine
Learning tasks such as classification and hypothesis testing, and
generalization to countable classes of i.i.d. models.Comment: 28 page
Solomonoff Induction Violates Nicod's Criterion
Nicod's criterion states that observing a black raven is evidence for the
hypothesis H that all ravens are black. We show that Solomonoff induction does
not satisfy Nicod's criterion: there are time steps in which observing black
ravens decreases the belief in H. Moreover, while observing any computable
infinite string compatible with H, the belief in H decreases infinitely often
when using the unnormalized Solomonoff prior, but only finitely often when
using the normalized Solomonoff prior. We argue that the fault is not with
Solomonoff induction; instead we should reject Nicod's criterion.Comment: ALT 201
Bayesian DNA copy number analysis
BACKGROUND: Some diseases, like tumors, can be related to chromosomal aberrations, leading to
changes of DNA copy number. The copy number of an aberrant genome can be represented as a
piecewise constant function, since it can exhibit regions of deletions or gains. Instead, in a healthy
cell the copy number is two because we inherit one copy of each chromosome from each our
parents.
Bayesian Piecewise Constant Regression (BPCR) is a Bayesian regression method for data that are
noisy observations of a piecewise constant function. The method estimates the unknown segment
number, the endpoints of the segments and the value of the segment levels of the underlying
piecewise constant function. The Bayesian Regression Curve (BRC) estimates the same data with
a smoothing curve. However, in the original formulation, some estimators failed to properly
determine the corresponding parameters. For example, the boundary estimator did not take into
account the dependency among the boundaries and succeeded in estimating more than one
breakpoint at the same position, losing segments.
RESULTS: We derived an improved version of the BPCR (called mBPCR) and BRC, changing the
segment number estimator and the boundary estimator to enhance the fitting procedure. We also
proposed an alternative estimator of the variance of the segment levels, which is useful in case of
data with high noise. Using artificial data, we compared the original and the modified version of
BPCR and BRC with other regression methods, showing that our improved version of BPCR
generally outperformed all the others. Similar results were also observed on real data.
CONCLUSION: We propose an improved method for DNA copy number estimation, mBPCR, which
performed very well compared to previously published algorithms. In particular, mBPCR was more
powerful in the detection of the true position of the breakpoints and of small aberrations in very
noisy data. Hence, from a biological point of view, our method can be very useful, for example, to
find targets of genomic aberrations in clinical cancer samples
Extreme State Aggregation Beyond MDPs
We consider a Reinforcement Learning setup where an agent interacts with an
environment in observation-reward-action cycles without any (esp.\ MDP)
assumptions on the environment. State aggregation and more generally feature
reinforcement learning is concerned with mapping histories/raw-states to
reduced/aggregated states. The idea behind both is that the resulting reduced
process (approximately) forms a small stationary finite-state MDP, which can
then be efficiently solved or learnt. We considerably generalize existing
aggregation results by showing that even if the reduced process is not an MDP,
the (q-)value functions and (optimal) policies of an associated MDP with same
state-space size solve the original problem, as long as the solution can
approximately be represented as a function of the reduced states. This implies
an upper bound on the required state space size that holds uniformly for all RL
problems. It may also explain why RL algorithms designed for MDPs sometimes
perform well beyond MDPs.Comment: 28 LaTeX pages. 8 Theorem
Revisiting the Core Ontology and Problem in Requirements Engineering
In their seminal paper in the ACM Transactions on Software Engineering and
Methodology, Zave and Jackson established a core ontology for Requirements
Engineering (RE) and used it to formulate the "requirements problem", thereby
defining what it means to successfully complete RE. Given that stakeholders of
the system-to-be communicate the information needed to perform RE, we show that
Zave and Jackson's ontology is incomplete. It does not cover all types of basic
concerns that the stakeholders communicate. These include beliefs, desires,
intentions, and attitudes. In response, we propose a core ontology that covers
these concerns and is grounded in sound conceptual foundations resting on a
foundational ontology. The new core ontology for RE leads to a new formulation
of the requirements problem that extends Zave and Jackson's formulation. We
thereby establish new standards for what minimum information should be
represented in RE languages and new criteria for determining whether RE has
been successfully completed.Comment: Appears in the proceedings of the 16th IEEE International
Requirements Engineering Conference, 2008 (RE'08). Best paper awar
Fermionic Molecular Dynamics for nuclear dynamics and thermodynamics
A new Fermionic Molecular Dynamics (FMD) model based on a Skyrme functional
is proposed in this paper. After introducing the basic formalism, some first
applications to nuclear structure and nuclear thermodynamics are presentedComment: 5 pages, Proceedings of the French-Japanese Symposium, September
2008. To be published in Int. J. of Mod. Phys.
A viscoelastic Rivlin-Ericksen material model applicable to glacier ice
We present a viscoelastic constitutive relation which describes transient creep of a modified second grade fluid enhanced with elastic properties of a solid. The material law describes a Rivlin-Ericksen material and is a generalization of existing material laws applied to study the viscoelastic properties of ice. The intention is to provide a formulation tailored to reproduce the viscoelastic behaviour of ice ranging from the instantaneous elastic response, to recoverable deformation, to viscous, stationary flow at the characteristic minimum creep rate associated with the deformation of polycrystalline ice. We numerically solve the problem of a slab of material shearing down a uniformly inclined plate. The equations are made dimensionless in a form in which elastic effects and/or the influence of higher order terms (i.e., strain accelerations) can be compared with viscous creep at the minimum creep rate by means of two dimensionless parameters. We discuss the resulting material behaviour and the features exhibited at different parameter combinations. Also, a viable range of the non-dimensional parameters is estimated in the scale analysis
Modelling debris flows down general channels
This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by Pudasaini and Hutter (2003). It is a generalisation of the Savage and Hutter (1989, 1991) equations based on simple channel topography to a two-phase fluid-solid mixture of debris material. Important terms emerging from the correct treatment of the kinematic and dynamic boundary condition, and the variable basal topography are systematically taken into account. For vanishing fluid contribution and torsion-free channel topography our new model equations exactly degenerate to the previous Savage-Hutter model equations while such a degeneration was not possible by the Iverson and Denlinger (2001) model, which, in fact, also aimed to extend the Savage and Hutter model. The model equations of this paper have been rigorously derived; they include the effects of the curvature and torsion of the topography, generally for arbitrarily curved and twisted channels of variable channel width. The equations are put into a standard conservative form of partial differential equations. From these one can easily infer the importance and influence of the pore-fluid-pressure distribution in debris flow dynamics. The solid-phase is modelled by applying a Coulomb dry friction law whereas the fluid phase is assumed to be an incompressible Newtonian fluid. Input parameters of the equations are the internal and bed friction angles of the solid particles, the viscosity and volume fraction of the fluid, the total mixture density and the pore pressure distribution of the fluid at the bed. Given the bed topography and initial geometry and the initial velocity profile of the debris mixture, the model equations are able to describe the dynamics of the depth profile and bed parallel depth-averaged velocity distribution from the initial position to the final deposit. A shock capturing, total variation diminishing numerical scheme is implemented to solve the highly non-linear equations. Simulation results present the combined effects of curvature, torsion and pore pressure on the dynamics of the flow over a general basal topography. These simulation results reveal new physical insight of debris flows over such non-trivial topography. Model equations are applied to laboratory avalanche and debris-flow-flume tests. Very good agreement between the theory and experiments is established
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