33 research outputs found
Zero-shot Task Preference Addressing Enabled by Imprecise Bayesian Continual Learning
Like generic multi-task learning, continual learning has the nature of
multi-objective optimization, and therefore faces a trade-off between the
performance of different tasks. That is, to optimize for the current task
distribution, it may need to compromise performance on some tasks to improve on
others. This means there exist multiple models that are each optimal at
different times, each addressing a distinct task-performance trade-off.
Researchers have discussed how to train particular models to address specific
preferences on these trade-offs. However, existing algorithms require
additional sample overheads -- a large burden when there are multiple, possibly
infinitely many, preferences. As a response, we propose Imprecise Bayesian
Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base
in the form of a convex hull of model parameter distributions and (2) obtains
particular models to address preferences with zero-shot. That is, IBCL does not
require any additional training overhead to construct preference-addressing
models from its knowledge base. We show that models obtained by IBCL have
guarantees in identifying the preferred parameters. Moreover, experiments show
that IBCL is able to locate the Pareto set of parameters given a preference,
maintain similar to better performance than baseline methods, and significantly
reduce training overhead via zero-shot preference addressing
Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods
The notion of uncertainty is of major importance in machine learning and
constitutes a key element of machine learning methodology. In line with the
statistical tradition, uncertainty has long been perceived as almost synonymous
with standard probability and probabilistic predictions. Yet, due to the
steadily increasing relevance of machine learning for practical applications
and related issues such as safety requirements, new problems and challenges
have recently been identified by machine learning scholars, and these problems
may call for new methodological developments. In particular, this includes the
importance of distinguishing between (at least) two different types of
uncertainty, often referred to as aleatoric and epistemic. In this paper, we
provide an introduction to the topic of uncertainty in machine learning as well
as an overview of attempts so far at handling uncertainty in general and
formalizing this distinction in particular.Comment: 59 page
Generalized belief change with imprecise probabilities and graphical models
We provide a theoretical investigation of probabilistic belief revision in complex frameworks, under extended conditions of uncertainty, inconsistency and imprecision. We motivate our kinematical approach by specializing our discussion to probabilistic reasoning with graphical models, whose modular representation allows for efficient inference. Most results in this direction are derived from the relevant work of Chan and Darwiche (2005), that first proved the inter-reducibility of virtual and probabilistic evidence. Such forms of information, deeply distinct in their meaning, are extended to the conditional and imprecise frameworks, allowing further generalizations, e.g. to experts' qualitative assessments. Belief aggregation and iterated revision of a rational agent's belief are also explored
Sparse Signal Recovery Based on Compressive Sensing and Exploration Using Multiple Mobile Sensors
The work in this dissertation is focused on two areas within the general discipline of statistical signal processing. First, several new algorithms are developed and exhaustively tested for solving the inverse problem of compressive sensing (CS). CS is a recently developed sub-sampling technique for signal acquisition and reconstruction which is more efficient than the traditional Nyquist sampling method. It provides the possibility of compressed data acquisition approaches to directly acquire just the important information of the signal of interest. Many natural signals are sparse or compressible in some domain such as pixel domain of images, time, frequency and so forth. The notion of compressibility or sparsity here means that many coefficients of the signal of interest are either zero or of low amplitude, in some domain, whereas some are dominating coefficients. Therefore, we may not need to take many direct or indirect samples from the signal or phenomenon to be able to capture the important information of the signal. As a simple example, one can think of a system of linear equations with N unknowns. Traditional methods suggest solving N linearly independent equations to solve for the unknowns. However, if many of the variables are known to be zero or of low amplitude, then intuitively speaking, there will be no need to have N equations. Unfortunately, in many real-world problems, the number of non-zero (effective) variables are unknown. In these cases, CS is capable of solving for the unknowns in an efficient way. In other words, it enables us to collect the important information of the sparse signal with low number of measurements. Then, considering the fact that the signal is sparse, extracting the important information of the signal is the challenge that needs to be addressed. Since most of the existing recovery algorithms in this area need some prior knowledge or parameter tuning, their application to real-world problems to achieve a good performance is difficult. In this dissertation, several new CS algorithms are proposed for the recovery of sparse signals. The proposed algorithms mostly do not require any prior knowledge on the signal or its structure. In fact, these algorithms can learn the underlying structure of the signal based on the collected measurements and successfully reconstruct the signal, with high probability. The other merit of the proposed algorithms is that they are generally flexible in incorporating any prior knowledge on the noise, sparisty level, and so on.
The second part of this study is devoted to deployment of mobile sensors in circumstances that the number of sensors to sample the entire region is inadequate. Therefore, where to deploy the sensors, to both explore new regions while refining knowledge in aleady visited areas is of high importance. Here, a new framework is proposed to decide on the trajectories of sensors as they collect the measurements. The proposed framework has two main stages. The first stage performs interpolation/extrapolation to estimate the phenomenon of interest at unseen loactions, and the second stage decides on the informative trajectory based on the collected and estimated data. This framework can be applied to various problems such as tuning the constellation of sensor-bearing satellites, robotics, or any type of adaptive sensor placement/configuration problem. Depending on the problem, some modifications on the constraints in the framework may be needed. As an application side of this work, the proposed framework is applied to a surrogate problem related to the constellation adjustment of sensor-bearing satellites