Search results for "Statistics - Machine Learning"
showing 10 items of 90 documents
Gap Filling of Biophysical Parameter Time Series with Multi-Output Gaussian Processes
2018
In this work we evaluate multi-output (MO) Gaussian Process (GP) models based on the linear model of coregionalization (LMC) for estimation of biophysical parameter variables under a gap filling setup. In particular, we focus on LAI and fAPAR over rice areas. We show how this problem cannot be solved with standard single-output (SO) GP models, and how the proposed MO-GP models are able to successfully predict these variables even in high missing data regimes, by implicitly performing an across-domain information transfer.
Disentangling Derivatives, Uncertainty and Error in Gaussian Process Models
2020
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems, especially in parameter retrieval. An addition to a predictive mean function, GPs come equipped with a useful property: the predictive variance function which provides confidence intervals for the predictions. The GP formulation usually assumes that there is no input noise in the training and testing points, only in the observations. However, this is often not the case in Earth observation problems where an accurate assessment of the instrument error is usually a…
Active emulation of computer codes with Gaussian processes – Application to remote sensing
2020
Many fields of science and engineering rely on running simulations with complex and computationally expensive models to understand the involved processes in the system of interest. Nevertheless, the high cost involved hamper reliable and exhaustive simulations. Very often such codes incorporate heuristics that ironically make them less tractable and transparent. This paper introduces an active learning methodology for adaptively constructing surrogate models, i.e. emulators, of such costly computer codes in a multi-output setting. The proposed technique is sequential and adaptive, and is based on the optimization of a suitable acquisition function. It aims to achieve accurate approximations…
The Weighted Tsetlin Machine: Compressed Representations with Weighted Clauses
2019
The Tsetlin Machine (TM) is an interpretable mechanism for pattern recognition that constructs conjunctive clauses from data. The clauses capture frequent patterns with high discriminating power, providing increasing expression power with each additional clause. However, the resulting accuracy gain comes at the cost of linear growth in computation time and memory usage. In this paper, we present the Weighted Tsetlin Machine (WTM), which reduces computation time and memory usage by weighting the clauses. Real-valued weighting allows one clause to replace multiple, and supports fine-tuning the impact of each clause. Our novel scheme simultaneously learns both the composition of the clauses an…
The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems
2019
The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression Tsetlin Machine (RTM). In all brevity, we modify the inner inference mechanism of the TM so that input patterns are transformed into a single continuous output, rather than to distinct categories. We achieve this by: (1) using the conjunctive clauses of the TM to capture arbitrarily complex patterns; (2) mapping these patterns to a continuous output through a novel voting and n…
The Convolutional Tsetlin Machine
2019
Convolutional neural networks (CNNs) have obtained astounding successes for important pattern recognition tasks, but they suffer from high computational complexity and the lack of interpretability. The recent Tsetlin Machine (TM) attempts to address this lack by using easy-to-interpret conjunctive clauses in propositional logic to solve complex pattern recognition problems. The TM provides competitive accuracy in several benchmarks, while keeping the important property of interpretability. It further facilitates hardware-near implementation since inputs, patterns, and outputs are expressed as bits, while recognition and learning rely on straightforward bit manipulation. In this paper, we ex…
Increasing the Inference and Learning Speed of Tsetlin Machines with Clause Indexing
2020
The Tsetlin Machine (TM) is a machine learning algorithm founded on the classical Tsetlin Automaton (TA) and game theory. It further leverages frequent pattern mining and resource allocation principles to extract common patterns in the data, rather than relying on minimizing output error, which is prone to overfitting. Unlike the intertwined nature of pattern representation in neural networks, a TM decomposes problems into self-contained patterns, represented as conjunctive clauses. The clause outputs, in turn, are combined into a classification decision through summation and thresholding, akin to a logistic regression function, however, with binary weights and a unit step output function. …
A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation
2020
The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and unity weights. Although the RTM has solved non-linear regression problems with competitive accuracy, the resolution of the output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To reduce this problem, we here introduce i…
Closed-Form Expressions for Global and Local Interpretation of Tsetlin Machines with Applications to Explaining High-Dimensional Data
2020
Tsetlin Machines (TMs) capture patterns using conjunctive clauses in propositional logic, thus facilitating interpretation. However, recent TM-based approaches mainly rely on inspecting the full range of clauses individually. Such inspection does not necessarily scale to complex prediction problems that require a large number of clauses. In this paper, we propose closed-form expressions for understanding why a TM model makes a specific prediction (local interpretability). Additionally, the expressions capture the most important features of the model overall (global interpretability). We further introduce expressions for measuring the importance of feature value ranges for continuous feature…
A General Framework for Complex Network-Based Image Segmentation
2019
International audience; With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image segmentation general framework using complex networks based community detection algorithms. If we consider regions as communities, using community detection algorithms directly can lead to an over-segmented image. To address this problem, we start by splitting the image into small regions using an initial segmentation. The obtained regions are used for building the complex network. To produce meaningful connected components and detect …