368 research outputs found
A Theory of the Risk for Optimization with Relaxation and its Application to Support Vector Machines
No full textIn this paper we consider optimization with relaxation, an ample paradigm to
make data-driven designs. This approach was previously considered by the same
authors of this work in Garatti and Campi (2019), a study that revealed a
deep-seated connection between two concepts: risk (probability of not
satisfying a new, out-of-sample, constraint) and complexity (according to a
definition introduced in paper Garatti and Campi (2019)). This connection was
shown to have profound implications in applications because it implied that the
risk can be estimated from the complexity, a quantity that can be measured from
the data without any knowledge of the data-generation mechanism. In the present
work we establish new results. First, we expand the scope of Garatti and Campi
(2019) so as to embrace a more general setup that covers various algorithms in
machine learning. Then, we study classical support vector methods - including
SVM (Support Vector Machine), SVR (Support Vector Regression) and SVDD (Support
Vector Data Description) - and derive new results for the ability of these
methods to generalize. All results are valid for any finite size of the data
set. When the sample size tends to infinity, we establish the unprecedented
result that the risk approaches the ratio between the complexity and the
cardinality of the data sample, regardless of the value of the complexity.Comment: https://www.jmlr.org/papers/v22/21-0641.htm
A theory of the risk for optimization with relaxation and its application to support vector machines
No full textIn this paper we consider optimization with relaxation, an ample paradigm to make data-driven designs. This approach was previously considered by the same authors of this work in Garatti and Campi (2019), a study that revealed a deep-seated connection between two concepts: risk (probability of not satisfying a new, out-of-sample, constraint) and complexity (according to a definition introduced in paper Garatti and Campi, 2019). This connection was shown to have profound implications in applications because it implied that the risk can be estimated from the complexity, a quantity that can be measured from the data without any knowledge of the data-generation mechanism. In the present work we establish new results. First, we expand the scope of Garatti and Campi (2019) so as to embrace a more general setup that covers various algorithms in machine learning. Then, we study classical support vector methods – including SVM (Support Vector Machine), SVR (Support Vector Regression) and SVDD (Support Vector Data Description) – and derive new results for the ability of these methods to generalize. All results are valid for any finite size of the data set. When the sample size tends to infinity, we establish the unprecedented result that the risk approaches the ratio between the complexity and the cardinality of the data sample, regardless of the value of the complexity
Analysis of the Kobe earthquake time series via system identification and fault-detection techniques
No full textFirst detection of acceleration and deceleration in protostellar Jets? Time variability in the Chamaeleontis II outflows
No full textContext. Kinematical and time variability studies of protostellar jets are fundamental for understanding the dynamics and the physics of these objects. Such studies remain very sporadic, since they require long baselines before they can be accomplished. Alms. We present for the first time a multi-epoch (20 years baseline) kinematical investigation of HH 52, 53, and 54 at optical and near-IR wavelengths, along with medium (optical) and high resolution (NIR) spectroscopic analyses, probing the kinematical and physical time variability conditions of the gas along the flows. Methods. By means of multi-epoch and multi-wavelength narrow-band images, we derived proper motions (PMs), tangential velocities, velocity and flux variability of the knots. Radial velocities and physical parameters of the gas were derived from spectroscopy. Finally, spatial velocities and inclination of the flows were obtained by combining both imaging and spectroscopy. Results. The PM analysis reveals three distinct, partially overlapping outflows. Spatial velocities of the knots vary from 50 km s -1 to 120 km s-1. The inclinations of the three flows are 58 ± 3°, 84 ± 2°, and 67 ± 3° (HH 52, HH 53, and HH 54 flows, respectively). In 20 years, about 60% of the observed knots show some degree of flux variability. Our set of observations apparently indicates acceleration and deceleration in a variety of knots along the jets. For about 20% of the knots, mostly coincident with working surfaces or interacting knots along the flows, a relevant variability in both flux and velocity is observed. We argue that both variabilities are related and that all or part of the kinetic energy lost by the interacting knots is successively radiated. The physical parameters derived from the diagnostics are quite homogeneous along and among the three outflows. The analysis indicates the presence of very light (NH � 103 cm-3), ionised (Te,. � 0.2-0.6), and hot (Te � 14000-26000 K) flows, impacting a denser medium. Several knots are deflected, especially in the HH 52 flow. At least for a couple of them (HH 54 G and GO), the deflection originates from the collision of the two. For the more massive parts of the flow, the deflection is likely the result of the flow collision with a dense cloud or with clumps. Finally, we discuss the possible driving sources of the flows. ©ESO 2009
Assessing the quality of identified models through the asymptotic theory - When is the result reliable?
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