Machine learning methods for constructing probabilistic <i>Fermi</i>-LAT catalogs

Modern Probabilistic Machine Learning and Control Methods for Portfolio Optimization

Many recent theoretical developments in the field of machine learning and control have rapidly expanded its relevance to a wide variety of applications. In particular, a variety of portfolio optimization problems have recently been considered as a promising application domain for machine learning and control methods. In highly uncertain and stochastic environments, portfolio optimization can be...

Probabilistic and On-line Methods in Machine Learning

On the surface, the three on-line machine learning problems analyzed in this thesis may seem unrelated. The first is an on-line investment strategy introduced by Tom Cover. We begin with a simple analysis that extends to the case of fixed-percentage transaction costs. We then describe an efficient implementation that runs in time polynomial in the number of stocks. The second problem is k-fold ...

Probabilistic machine learning

Probabilistic Catalogs for Crowded Stellar Fields

We introduce a probabilistic (Bayesian) method for producing catalogs from images of crowded stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by overlapping sources. The luminosity function of the stars can also be inferred even when the precise luminosity of each star is uncertain. This is in contrast with sta...

New methods for constructing shellable simplicial complexes

A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...