On the force of V2 declaratives

This paper discusses a variant of German V2 declaratives sharing properties with both subordinate relative clauses and main clauses. I argue that modal subordination failure helps decide between two rivaling accounts for this construction. Thus, a hypotactic analysis involving syntactic variable sharing must be preferred over parataxis plus anaphora resolution. The scopal behavior of the construction will be derived from its 'proto-assertional force,' which it shares with similar 'embedded root' constructions

An Exponential Lower Bound on the Complexity of Regularization Paths

For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadratic programs that are parameterized by a single parameter, as for example the Support Vector Machine (SVM). Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but the entire path of solutions, making the selection of an optimal parameter much easier. It has been assumed that these piecewise linear solution paths have only linear complexity, i.e. linearly many bends. We prove that for the support vector machine this complexity can be exponential in the number of training points in the worst case. More strongly, we construct a single instance of n input points in d dimensions for an SVM such that at least \Theta(2^{n/2}) = \Theta(2^d) many distinct subsets of support vectors occur as the regularization parameter changes.Comment: Journal version, 28 Pages, 5 Figure

On Covert Modality in German Root Infinitives

German adult Bare Root Infinitives (BRIs) share a considerable number of uses with imperatives. They can, for example, be employed as commands, (1a), instructions, (1b), and permissions, (1c). In addition, they may occur as (self-directed) wishes, (1d) (for an overview, see Gärtner 2013, an

Überlegungen zur versteckten Modalität infiniter Hauptsatzstrukturen

Die folgenden Überlegungen widmen sich verschiedenen Ansätzen zur Behandlung versteckter Modalität bei infiniten Hauptsatzstrukturen. Dabei stehen zu-lose Infinitive im Zentrum. Im Rahmen der Theorie der „Transparenten Logischen Form“ (von Stechow 1993; 2004) wird eine formalisierte Version des Inferenzansatzes von Reis (1995; 2003) entwickelt, in dem pragmatische Anreicherung als Bindung einer Weltvariable per existentiellem Abschluss formulierbar ist. Es wird gezeigt, dass dieser Mechanismus nicht ohne weiteres auf interrogativische Hauptsatzinfinitive übertragbar ist. Dieselbe Schwierigkeit wird in einem zweiten Schritt an dem auf einem volitionalen Einstellungsoperator aufbauenden Illokutionsansatz von Truckenbrodt (2006a; 2006b) nachgewiesen. Der anschließende kurze Diskussionsteil bespricht Lesarten und Verwendungen von Hauptsatzinfinitiven, wobei performative Modalität, modale Kraft und konzessive sowie optativ-desiderative Sprechakte besonders berücksichtigt sind

Strange Loops: Phrase-Linking Grammar Meets Kaynean Pronominalization

As shown earlier by Gärtner (2002), linked trees, the graphs used by Phrase-Linking Grammar (Peters & Ritchie 1981) to capture (unbounded) dependencies, can be cyclic under the special condition that two „displaced“ constituents end up as sisters of each other. Such „PLG-loops“ closely match the particular kind of crossing dependency familiar from Bach-Peters sentences. We will show how PLG-loops allow implementing Bach-Peters configurations within the movement-based approach to binding by Kayne (2002). The resulting structures correspond to QR-derived adjunction structures of the kind introduced by May (1985)

Screening Rules for Convex Problems

We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point, the structure of the objective function and the duality gap is used to gather information on the optimal solution. In the second step, this information is used to produce screening rules, i.e. safely identifying unimportant weight variables of the optimal solution. Our general framework leads to a large variety of useful existing as well as new screening rules for many applications. For example, we provide new screening rules for general simplex and $L_1$-constrained problems, Elastic Net, squared-loss Support Vector Machines, minimum enclosing ball, as well as structured norm regularized problems, such as group lasso