206,178 research outputs found
SOM-VAE: Interpretable Discrete Representation Learning on Time Series
High-dimensional time series are common in many domains. Since human
cognition is not optimized to work well in high-dimensional spaces, these areas
could benefit from interpretable low-dimensional representations. However, most
representation learning algorithms for time series data are difficult to
interpret. This is due to non-intuitive mappings from data features to salient
properties of the representation and non-smoothness over time. To address this
problem, we propose a new representation learning framework building on ideas
from interpretable discrete dimensionality reduction and deep generative
modeling. This framework allows us to learn discrete representations of time
series, which give rise to smooth and interpretable embeddings with superior
clustering performance. We introduce a new way to overcome the
non-differentiability in discrete representation learning and present a
gradient-based version of the traditional self-organizing map algorithm that is
more performant than the original. Furthermore, to allow for a probabilistic
interpretation of our method, we integrate a Markov model in the representation
space. This model uncovers the temporal transition structure, improves
clustering performance even further and provides additional explanatory
insights as well as a natural representation of uncertainty. We evaluate our
model in terms of clustering performance and interpretability on static
(Fashion-)MNIST data, a time series of linearly interpolated (Fashion-)MNIST
images, a chaotic Lorenz attractor system with two macro states, as well as on
a challenging real world medical time series application on the eICU data set.
Our learned representations compare favorably with competitor methods and
facilitate downstream tasks on the real world data.Comment: Accepted for publication at the Seventh International Conference on
Learning Representations (ICLR 2019
Robust Kalman Filtering: Asymptotic Analysis of the Least Favorable Model
We consider a robust filtering problem where the robust filter is designed
according to the least favorable model belonging to a ball about the nominal
model. In this approach, the ball radius specifies the modeling error tolerance
and the least favorable model is computed by performing a Riccati-like backward
recursion. We show that this recursion converges provided that the tolerance is
sufficiently small
Projective system approach to the martingale characterization of the absence of arbitrage
The equivalence between the absence of arbitrage and the existence of an equivalent martingale measure fails when an infinite number of trading dates is considered. By enlarging the set of states of nature and the probability measure through a projective system of topological spaces and Radon measures, we characterize the absence of arbitrage when the time set is countable
An Efficient Search Strategy for Aggregation and Discretization of Attributes of Bayesian Networks Using Minimum Description Length
Bayesian networks are convenient graphical expressions for high dimensional
probability distributions representing complex relationships between a large
number of random variables. They have been employed extensively in areas such
as bioinformatics, artificial intelligence, diagnosis, and risk management. The
recovery of the structure of a network from data is of prime importance for the
purposes of modeling, analysis, and prediction. Most recovery algorithms in the
literature assume either discrete of continuous but Gaussian data. For general
continuous data, discretization is usually employed but often destroys the very
structure one is out to recover. Friedman and Goldszmidt suggest an approach
based on the minimum description length principle that chooses a discretization
which preserves the information in the original data set, however it is one
which is difficult, if not impossible, to implement for even moderately sized
networks. In this paper we provide an extremely efficient search strategy which
allows one to use the Friedman and Goldszmidt discretization in practice
Option Pricing with Delayed Information
We propose a model to study the effects of delayed information on option
pricing. We first talk about the absence of arbitrage in our model, and then
discuss super replication with delayed information in a binomial model,
notably, we present a closed form formula for the price of convex contingent
claims. Also, we address the convergence problem as the time-step and delay
length tend to zero and introduce analogous results in the continuous time
framework. Finally, we explore how delayed information exaggerates the
volatility smile
- …