When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. T...

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix X. Like the well-known result of Zou et al. (2007), which gives the degrees of freedom of the lasso fit when X has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitr...

This paper investigates the degrees of freedom of the interference channel in the presence of a dedicated MIMO relay. The relay is used to manage the interference at the receivers. It is assumed that all nodes including the relay have channel state information only for their own links and that the relay has M ≥ K antennas in a K-user network. We pose the question: What is the benefit of exploit...

To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model selection. We argue that, on the contrary, model complexity and degrees of freedom may correspond very poorly. We exhibit and theoretically explore various fit...

Degrees of freedom is a fundamental concept in statistical modeling, as it provides a quantitative description of the amount of fitting performed by a given procedure. But, despite this fundamental role in statistics, its behavior is not completely well-understood, even in somewhat basic settings. For example, it may seem intuitively obvious that the best subset selection fit with subset size k...

There are many design factors and choices when mounting a vision system for robot control. Such factors may include the kinematic and dynamic characteristics in the robot’s degrees of freedom (DOF), which determine at what velocities and fields-of-view a camera can achieve. Another factor is that additional motion components (such as pan-tilt units) are often mounted on a robot and introduce sy...

∗Thanks to audiences at Tufts University, the University of Kentucky, and the University of Toronto for helpful comments and questions. Special thanks to Benj Hellie and Jonathan McCoy for detailed feedback on previous versions, and to Robert Axtell, whose suggestion that reductions in degrees of freedom play a role in the physically unproblematic emergence of complex systems (made during the 2...

Degrees of freedom (DOF) refer to the number of free parameters in a model that need to be independently controlled for generating intended output. In this paper, we discuss how DOF is a critical issue not only for computational modeling, but also for theoretical understanding of prosody. The relevance of DOF is examined from the perspective of the motor control of articulatory movements, the a...