Chapter 37 Improv, Stand-Up, and Comedy

The idea of improvisation, broadly defined, has been integral to our imagination of the medieval musical past. It can be related to many elements of production: to the act of un-notated creation; to the manipulation and amplification of notated materials; to our observance of rigid rules and formulae; or to spontaneous freedom. Likely a product of the Carolingian Renaissance, this is the first medieval music treatise to address an aspect of chant performance that does not only relate to a memorized repertoire, but includes an unwritten practice of extemporizing an accompanying voice to a pre-given melody. The art of “coloration” or the ornamentation of a line, whether polyphonic or monophonic, had been an integral part of extemporization since at least the time of the Ad organum faciendum treatises. When planning author's ontological inquiries, the author's would do well to remember the possible existence of creativity that is not inspired, or ephemerality that is not performer- or expression-centered

Sampling Correctors

In many situations, sample data is obtained from a noisy or imperfect source. In order to address such corruptions, this paper introduces the concept of a sampling corrector. Such algorithms use structure that the distribution is purported to have, in order to allow one to make "on-the-fly" corrections to samples drawn from probability distributions. These algorithms then act as filters between the noisy data and the end user. We show connections between sampling correctors, distribution learning algorithms, and distribution property testing algorithms. We show that these connections can be utilized to expand the applicability of known distribution learning and property testing algorithms as well as to achieve improved algorithms for those tasks. As a first step, we show how to design sampling correctors using proper learning algorithms. We then focus on the question of whether algorithms for sampling correctors can be more efficient in terms of sample complexity than learning algorithms for the analogous families of distributions. When correcting monotonicity, we show that this is indeed the case when also granted query access to the cumulative distribution function. We also obtain sampling correctors for monotonicity without this stronger type of access, provided that the distribution be originally very close to monotone (namely, at a distance $O(1/\log^2 n)$). In addition to that, we consider a restricted error model that aims at capturing "missing data" corruptions. In this model, we show that distributions that are close to monotone have sampling correctors that are significantly more efficient than achievable by the learning approach. We also consider the question of whether an additional source of independent random bits is required by sampling correctors to implement the correction process

Chapter 37 Improv, Stand-Up, and Comedy

The idea of improvisation, broadly defined, has been integral to our imagination of the medieval musical past. It can be related to many elements of production: to the act of un-notated creation; to the manipulation and amplification of notated materials; to our observance of rigid rules and formulae; or to spontaneous freedom. Likely a product of the Carolingian Renaissance, this is the first medieval music treatise to address an aspect of chant performance that does not only relate to a memorized repertoire, but includes an unwritten practice of extemporizing an accompanying voice to a pre-given melody. The art of “coloration” or the ornamentation of a line, whether polyphonic or monophonic, had been an integral part of extemporization since at least the time of the Ad organum faciendum treatises. When planning author's ontological inquiries, the author's would do well to remember the possible existence of creativity that is not inspired, or ephemerality that is not performer- or expression-centered

An adaptivity hierarchy theorem for property testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers received to prior queries, and their non-adaptive counterparts, in which all queries are independent of answers obtained from previous queries. In this work, we investigate the role of adaptivity in property testing at a finer level. We first quantify the degree of adaptivity of a testing algorithm by considering the number of "rounds of adaptivity" it uses. More accurately, we say that a tester is k-(round) adaptive if it makes queries in k+1 rounds, where the queries in the i'th round may depend on the answers obtained in the previous i-1 rounds. Then, we ask the following question: Does the power of testing algorithms smoothly grow with the number of rounds of adaptivity? We provide a positive answer to the foregoing question by proving an adaptivity hierarchy theorem for property testing. Specifically, our main result shows that for every n in N and 0 <= k <= n^{0.99} there exists a property Pi_{n,k} of functions for which (1) there exists a k-adaptive tester for Pi_{n,k} with query complexity tilde O(k), yet (2) any (k-1)-adaptive tester for Pi_{n,k} must make Omega(n) queries. In addition, we show that such a qualitative adaptivity hierarchy can be witnessed for testing natural properties of graphs

Generalized uniformity testing

In this work, we revisit the problem of uniformity testing of discrete probability distributions. A fundamental problem in distribution testing, testing uniformity over a known domain has been addressed over a significant line of works, and is by now fully understood. The complexity of deciding whether an unknown distribution is uniform over its unknown (and arbitrary) support, however, is much less clear. Yet, this task arises as soon as no prior knowledge on the domain is available, or whenever the samples originate from an unknown and unstructured universe. In this work, we introduce and study this generalized uniformity testing question, and establish nearly tight upper and lower bound showing that – quite surprisingly – its sample complexity significantly differs from the known-domain case. Moreover, our algorithm is intrinsically adaptive, in contrast to the overwhelming majority of known distribution testing algorithms

Matthieu Saladin, Esthétique de l’improvisation libre. Expérimentation musicale et politique

L’ouvrage de Matthieu Saladin est une contribution importante au champ aujourd’hui très dynamique des études sur l’improvisation (voir Lewis & Piekut, 2015). À travers trois collectifs ayant occupé une place essentielle dans le développement des musiques improvisées au tournant des années 1970 – l’AMM, le Spontaneous Music Ensemble (SME) et le Musica Elettronica Viva (MEV) – l’auteur entreprend d’analyser l’esthétique sous-jacente à la pratique alors émergente de l’improvisation dite « libre ..

Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine

Private closeness testing asks to decide whether the underlying probability distributions of two sensitive datasets are identical or differ significantly in statistical distance, while guaranteeing (differential) privacy of the data. As in most (if not all) distribution testing questions studied under privacy constraints, however, previous work assumes that the two datasets are equally sensitive, i.e., must be provided the same privacy guarantees. This is often an unrealistic assumption, as different sources of data come with different privacy requirements; as a result, known closeness testing algorithms might be unnecessarily conservative, "paying" too high a privacy budget for half of the data. In this work, we initiate the study of the closeness testing problem under heterogeneous privacy constraints, where the two datasets come with distinct privacy requirements. We formalize the question and provide algorithms under the three most widely used differential privacy settings, with a particular focus on the local and shuffle models of privacy; and show that one can indeed achieve better sample efficiency when taking into account the two different "epsilon" requirements