Real-world datasets are often characterised by outliers, points far from the majority of the points, which might negatively influence modelling of the data. In data analysis it is hence important to use methods that are robust to outliers. In this paper we develop a robust regression method for finding the largest subset in the data that can be approximated using a sparse linear model to a given precision. We show that the problem is NP-hard and hard to approximate. We present an efficient algorithm, termed slise, to find solutions to the problem. Our method extends current state-of-the-art robust regression methods, especially in terms of scalability on large datasets. Furthermore, we show that our method can be used to yield interpretable explanations for individual decisions by opaque, black box, classifiers. Our approach solves shortcomings in other recent explanation methods by not requiring sampling of new data points and by being usable without modifications across various data domains. We demonstrate our method using both synthetic and real-world regression and classification problems.
Affordable material extrusion (ME) desktop 3D printers have gained wide popularity in recent decade with growing markets. 1 These printers are often used in educational institutions, libraries and enterprise engineering, marketing, and creative departments as well as by hobbyists. Concurrently as larger manufacturing companies are developing their own closed software printing systems, open software and hardware development is also underway. 2 With open-source 3D printers, users may change code, use different, perhaps completely new materials and printers such as RepRap can be modified by the user. 3 Even affordable open-source metal printers are possible in the future. 4 These trends are very meaningful especially when the number of people who have access to the 3D printing grows larger and larger and the need of knowledge on safety related to 3D printing grows.Desktop 3D printers based on ME have been shown to emit nanoparticles in number of studies. [5][6][7][8][9][10][11] Also, gas-phase compounds, depending on the material, may be emitted during 3D printing. 10,12,13 Emissions are dependent mainly on the chemical composition of the 3D printing filament and nozzle temperature. 5,7,10 In addition, 3D printer malfunctions have been shown to affect the emissions. 9,10
In recent years the use of complex machine learning has increased drastically. These complex black box models trade interpretability for accuracy. The lack of interpretability is troubling for, e.g., socially sensitive, safety-critical, or knowledge extraction applications. In this paper, we propose a new explanation method, SLISE, for interpreting predictions from black box models. SLISE can be used with any black box model (model-agnostic), does not require any modifications to the black box model (post-hoc), and explains individual predictions (local). We evaluate our method using real-world datasets and compare it against other model-agnostic, local explanation methods. Our approach solves shortcomings in other related explanation methods by only using existing data instead of sampling new, artificial data. The method also generates more generalizable explanations and is usable without modification across various data domains.
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