12 research outputs found
Adaptive Optimization Algorithms for Machine Learning
Machine learning assumes a pivotal role in our data-driven world. The
increasing scale of models and datasets necessitates quick and reliable
algorithms for model training. This dissertation investigates adaptivity in
machine learning optimizers. The ensuing chapters are dedicated to various
facets of adaptivity, including: 1. personalization and user-specific models
via personalized loss, 2. provable post-training model adaptations via
meta-learning, 3. learning unknown hyperparameters in real time via
hyperparameter variance reduction, 4. fast O(1/k^2) global convergence of
second-order methods via stepsized Newton method regardless of the
initialization and choice basis, 5. fast and scalable second-order methods via
low-dimensional updates. This thesis contributes novel insights, introduces new
algorithms with improved convergence guarantees, and improves analyses of
popular practical algorithms.Comment: Dissertation thesi
Exponential families on resource-constrained systems
This work is about the estimation of exponential family models on resource-constrained
systems. Our main goal is learning probabilistic models on devices with highly restricted
storage, arithmetic, and computational capabilities—so called, ultra-low-power
devices. Enhancing the learning capabilities of such devices opens up opportunities for
intelligent ubiquitous systems in all areas of life, from medicine, over robotics, to home
automation—to mention just a few. We investigate the inherent resource consumption of
exponential families, review existing techniques, and devise new methods to reduce the
resource consumption. The resource consumption, however, must not be reduced at all
cost. Exponential families possess several desirable properties that must be preserved:
Any probabilistic model encodes a conditional independence structure—our methods
keep this structure intact. Exponential family models are theoretically well-founded.
Instead of merely finding new algorithms based on intuition, our models are formalized
within the framework of exponential families and derived from first principles. We do
not introduce new assumptions which are incompatible with the formal derivation of the
base model, and our methods do not rely on properties of particular high-level applications.
To reduce the memory consumption, we combine and adapt reparametrization
and regularization in an innovative way that facilitates the sparse parametrization of
high-dimensional non-stationary time-series. The procedure allows us to load models in
memory constrained systems, which would otherwise not fit. We provide new theoretical
insights and prove that the uniform distance between the data generating process
and our reparametrized solution is bounded. To reduce the arithmetic complexity of
the learning problem, we derive the integer exponential family, based on the very definition
of sufficient statistics and maximum entropy estimation. New integer-valued
inference and learning algorithms are proposed, based on variational inference, proximal
optimization, and regularization. The benefit of this technique is larger, the weaker
the underlying system is, e.g., the probabilistic inference on a state-of-the-art ultra-lowpower
microcontroller can be accelerated by a factor of 250. While our integer inference
is fast, the underlying message passing relies on the variational principle, which is inexact
and has unbounded error on general graphs. Since exact inference and other existing
methods with bounded error exhibit exponential computational complexity, we employ
near minimax optimal polynomial approximations to yield new stochastic algorithms
for approximating the partition function and the marginal probabilities. Changing the
polynomial degree allows us to control the complexity and the error of our new stochastic
method. We provide an error bound that is parametrized by the number of samples, the
polynomial degree, and the norm of the model’s parameter vector. Moreover, important
intermediate quantities can be precomputed and shared with the weak computational device
to reduce the resource requirement of our method even further. All new techniques
are empirically evaluated on synthetic and real-world data, and the results confirm the
properties which are predicted by our theoretical derivation. Our novel techniques allow
a broader range of models to be learned on resource-constrained systems and imply
several new research possibilities
Handbook of Mathematical Geosciences
This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum