1,893 research outputs found
Dynamic Adaptation on Non-Stationary Visual Domains
Domain adaptation aims to learn models on a supervised source domain that
perform well on an unsupervised target. Prior work has examined domain
adaptation in the context of stationary domain shifts, i.e. static data sets.
However, with large-scale or dynamic data sources, data from a defined domain
is not usually available all at once. For instance, in a streaming data
scenario, dataset statistics effectively become a function of time. We
introduce a framework for adaptation over non-stationary distribution shifts
applicable to large-scale and streaming data scenarios. The model is adapted
sequentially over incoming unsupervised streaming data batches. This enables
improvements over several batches without the need for any additionally
annotated data. To demonstrate the effectiveness of our proposed framework, we
modify associative domain adaptation to work well on source and target data
batches with unequal class distributions. We apply our method to several
adaptation benchmark datasets for classification and show improved classifier
accuracy not only for the currently adapted batch, but also when applied on
future stream batches. Furthermore, we show the applicability of our
associative learning modifications to semantic segmentation, where we achieve
competitive results
Canonical Quantization and Impenetrable Barriers
We address an apparent conflict between the traditional canonical
quantization framework of quantum theory and the spatially restricted quantum
dynamics, when the translation invariance of the otherwise free quantum system
is broken by boundary conditions. By invoking an exemplary case of a particle
in an infinite well, we analyze spectral problems for related, confined and
global, observables. In particular, we show how one can make sense of various
operators pertaining to trapped particles by not ignoring the rest of the real
line (e.g., that space which is never occupied by the particle in question).Comment: to appear in Am.J.Phys (2004
Transition times and stochastic resonance for multidimensional diffusions with time periodic drift: A large deviations approach
We consider potential type dynamical systems in finite dimensions with two
meta-stable states. They are subject to two sources of perturbation: a slow
external periodic perturbation of period and a small Gaussian random
perturbation of intensity , and, therefore, are mathematically
described as weakly time inhomogeneous diffusion processes. A system is in
stochastic resonance, provided the small noisy perturbation is tuned in such a
way that its random trajectories follow the exterior periodic motion in an
optimal fashion, that is, for some optimal intensity . The
physicists' favorite, measures of quality of periodic tuning--and thus
stochastic resonance--such as spectral power amplification or signal-to-noise
ratio, have proven to be defective. They are not robust w.r.t. effective model
reduction, that is, for the passage to a simplified finite state Markov chain
model reducing the dynamics to a pure jumping between the meta-stable states of
the original system. An entirely probabilistic notion of stochastic resonance
based on the transition dynamics between the domains of attraction of the
meta-stable states--and thus failing to suffer from this robustness defect--was
proposed before in the context of one-dimensional diffusions. It is
investigated for higher-dimensional systems here, by using extensions and
refinements of the Freidlin--Wentzell theory of large deviations for time
homogeneous diffusions. Large deviations principles developed for weakly time
inhomogeneous diffusions prove to be key tools for a treatment of the problem
of diffusion exit from a domain and thus for the approach of stochastic
resonance via transition probabilities between meta-stable sets.Comment: Published at http://dx.doi.org/10.1214/105051606000000385 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Logic, Probability and Action: A Situation Calculus Perspective
The unification of logic and probability is a long-standing concern in AI,
and more generally, in the philosophy of science. In essence, logic provides an
easy way to specify properties that must hold in every possible world, and
probability allows us to further quantify the weight and ratio of the worlds
that must satisfy a property. To that end, numerous developments have been
undertaken, culminating in proposals such as probabilistic relational models.
While this progress has been notable, a general-purpose first-order knowledge
representation language to reason about probabilities and dynamics, including
in continuous settings, is still to emerge. In this paper, we survey recent
results pertaining to the integration of logic, probability and actions in the
situation calculus, which is arguably one of the oldest and most well-known
formalisms. We then explore reduction theorems and programming interfaces for
the language. These results are motivated in the context of cognitive robotics
(as envisioned by Reiter and his colleagues) for the sake of concreteness.
Overall, the advantage of proving results for such a general language is that
it becomes possible to adapt them to any special-purpose fragment, including
but not limited to popular probabilistic relational models
Pseudo generators of spatial transfer operators
Metastable behavior in dynamical systems may be a significant challenge for a
simulation based analysis. In recent years, transfer operator based approaches
to problems exhibiting metastability have matured. In order to make these
approaches computationally feasible for larger systems, various reduction
techniques have been proposed: For example, Sch\"utte introduced a spatial
transfer operator which acts on densities on configuration space, while Weber
proposed to avoid trajectory simulation (like Froyland et al.) by considering a
discrete generator.
In this manuscript, we show that even though the family of spatial transfer
operators is not a semigroup, it possesses a well defined generating structure.
What is more, the pseudo generators up to order 4 in the Taylor expansion of
this family have particularly simple, explicit expressions involving no
momentum averaging. This makes collocation methods particularly easy to
implement and computationally efficient, which in turn may open the door for
further efficiency improvements in, e.g., the computational treatment of
conformation dynamics. We experimentally verify the predicted properties of
these pseudo generators by means of two academic examples
Abstracting Noisy Robot Programs
Abstraction is a commonly used process to represent some low-level system by
a more coarse specification with the goal to omit unnecessary details while
preserving important aspects. While recent work on abstraction in the situation
calculus has focused on non-probabilistic domains, we describe an approach to
abstraction of probabilistic and dynamic systems. Based on a variant of the
situation calculus with probabilistic belief, we define a notion of
bisimulation that allows to abstract a detailed probabilistic basic action
theory with noisy actuators and sensors by a possibly deterministic basic
action theory. By doing so, we obtain abstract Golog programs that omit
unnecessary details and which can be translated back to a detailed program for
actual execution. This simplifies the implementation of noisy robot programs,
opens up the possibility of using deterministic reasoning methods (e.g.,
planning) on probabilistic problems, and provides domain descriptions that are
more easily understandable and explainable
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