Learning parametric dictionaries for graph signals

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification

The Self-Organisation of Strategic Alliances

Strategic alliances form a vital part of today's business environment. The sheer variety of collaborative forms is notable - which include R&D coalitions, marketing and distribution agreements, franchising, co-production agreements, licensing, consortiums and joint ventures. Here we define a strategic alliance as a cooperative agreement between two or more autonomous firms pursuing common objectives or working towards solving common problems through a period of sustained interaction. A distinction is commonly made between 'formal' and 'informal' inter-firm alliances. Informal alliances involve voluntary contact and interaction while in formal alliances cooperation is governed by a contractual agreement. The advantage of formal alliances is the ability to put in place IPR clauses, confidentially agreements and other contractual measures designed to safeguard the firm against knowledge spill-over. However, these measures are costly to instigate and police. By contrast, a key attraction of informal relationships is their low co-ordination costs. Informal know-how trading is relatively simple, uncomplicated and more flexible, and has been observed in a number of industries. A number of factors affecting firms' decisions to cooperate or not cooperate within strategic alliances have been raised in the literature. In this paper we consider three factors in particular: the relative costs of coordinating activity through strategic alliances vis-a-vis the costs of coordinating activity in-house, the degree of uncertainty present in the competitive environment, and the feedback between individual decision-making and industry structure. Whereas discussion of the first two factors is well developed in the strategic alliance literature, the third factor has hitherto only been addressed indirectly. The contribution to this under-researched area represents an important contribution of this paper to the current discourse. In order to focus the discussion, the paper considers the formation of horizontal inter-firm strategic alliances in dynamic product markets. These markets are characterised by rapid rates of technological change, a high degree of market uncertainty, and high rewards (supernormal profits) for successful firms offset by shortening life cycles.Strategic Alliances, Innovation Networks, Self-Organisation

Inferring processes of cultural transmission: the critical role of rare variants in distinguishing neutrality from novelty biases

Neutral evolution assumes that there are no selective forces distinguishing different variants in a population. Despite this striking assumption, many recent studies have sought to assess whether neutrality can provide a good description of different episodes of cultural change. One approach has been to test whether neutral predictions are consistent with observed progeny distributions, recording the number of variants that have produced a given number of new instances within a specified time interval: a classic example is the distribution of baby names. Using an overlapping generations model we show that these distributions consist of two phases: a power law phase with a constant exponent of -3/2, followed by an exponential cut-off for variants with very large numbers of progeny. Maximum likelihood estimations of the model parameters provide a direct way to establish whether observed empirical patterns are consistent with neutral evolution. We apply our approach to a complete data set of baby names from Australia. Crucially we show that analyses based on only the most popular variants, as is often the case in studies of cultural evolution, can provide misleading evidence for underlying transmission hypotheses. While neutrality provides a plausible description of progeny distributions of abundant variants, rare variants deviate from neutrality. Further, we develop a simulation framework that allows for the detection of alternative cultural transmission processes. We show that anti-novelty bias is able to replicate the complete progeny distribution of the Australian data set

NetLSD: Hearing the Shape of a Graph

Comparison among graphs is ubiquitous in graph analytics. However, it is a hard task in terms of the expressiveness of the employed similarity measure and the efficiency of its computation. Ideally, graph comparison should be invariant to the order of nodes and the sizes of compared graphs, adaptive to the scale of graph patterns, and scalable. Unfortunately, these properties have not been addressed together. Graph comparisons still rely on direct approaches, graph kernels, or representation-based methods, which are all inefficient and impractical for large graph collections. In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation method that allows for straightforward comparisons of large graphs. NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph. Our evaluation on a variety of real-world graphs demonstrates that it outperforms previous works in both expressiveness and efficiency.Comment: KDD '18: The 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, August 19--23, 2018, London, United Kingdo

Identification of Network Externalities in Markets for Non-Durables

This paper introduces a structural econometric model of consumer demand for non-durable goods, which exhibits network externalities. The structural model allows us to identify the parameters, which determine the strength of the externalities in the underlying economic model from the empirical estimation results. The estimates of these parameters can then be employed to test the economic significance of the externalities and the compatibility of networks. The identifying assumption that drives our results is that consumers care about the lagged instead of the current network size. We argue that it does not necessarily bound their rationality. To complete our structural model, we provide an example of functional specification that yields a simple linear stochastic model of demand. Using this functional specification, we identify all structural parameters of the model. In the end, the estimation and the stochastic structure of the resulting econometric model are discussed. ZUSAMMENFASSUNG - ( Identifikation der Netzwerkeffekten in den Märkten für nicht-dauerhafte Güter) Der vorliegende Beitrag stellt ein strukturelles ökonometrisches Modell der Konsumnachfrage für nicht-dauerhafte Güter mit externen Netzwerkeffekten vor. Das strukturelle Modell lässt uns die Parameter von Netzwerkeffekten im zugrunde liegenden ökonomischen Modell empirisch zu identifizieren. Die Schätzer der Strukturparameter könnten für das Testen der Netzwerkkompatibilität und der ökonomischen Signifikanz der Netzwerkeffekte verwendet werden. Für die Identifikation nehmen wir an, dass die Konsumenten die Netzwerksgröße verzögert wahrnehmen. Wir argumentieren, dass diese Annahme nicht notwendigerweise mit irrationalem Verhalten gleichzusetzen ist. Um das strukturelle Modell zu vollständigen, geben wir eine funktionale Spezifikation, aus der ein lineares stochastisches Nachfragemodell folgt. Unter Verwendung dieser Spezifikation sind alle Strukturparameter von dem Modell identifiziert. Zum Schluss diskutieren wir die Schätzung und die stochastische Struktur des sich ergebenden ökonometrischen Modells.Structural Econometric Model, Network Externalities, Innovation Diffusion

Learning theories reveal loss of pancreatic electrical connectivity in diabetes as an adaptive response

Cells of almost all solid tissues are connected with gap junctions which permit the direct transfer of ions and small molecules, integral to regulating coordinated function in the tissue. The pancreatic islets of Langerhans are responsible for secreting the hormone insulin in response to glucose stimulation. Gap junctions are the only electrical contacts between the beta-cells in the tissue of these excitable islets. It is generally believed that they are responsible for synchrony of the membrane voltage oscillations among beta-cells, and thereby pulsatility of insulin secretion. Most attempts to understand connectivity in islets are often interpreted, bottom-up, in terms of measurements of gap junctional conductance. This does not, however explain systematic changes, such as a diminished junctional conductance in type 2 diabetes. We attempt to address this deficit via the model presented here, which is a learning theory of gap junctional adaptation derived with analogy to neural systems. Here, gap junctions are modelled as bonds in a beta-cell network, that are altered according to homeostatic rules of plasticity. Our analysis reveals that it is nearly impossible to view gap junctions as homogeneous across a tissue. A modified view that accommodates heterogeneity of junction strengths in the islet can explain why, for example, a loss of gap junction conductance in diabetes is necessary for an increase in plasma insulin levels following hyperglycemia.Comment: 15 pages, 5 figures. To appear in PLoS One (2013

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

A Neural Network Model for the Development of Simple and Complex Cell Receptive Fields Within Cortical Maps of Orientation and Ocular Dominance

Prenatal development of the primary visual cortex leads to simple cells with spatially distinct and oriented ON and OFF subregions. These simple cells are organized into spatial maps of orientation and ocular dominance that exhibit singularities, fractures, and linear zones. On a finer spatial scale, simple cells occur that are sensitive to similar orientations but opposite contrast polarities, and exhibit both even-symmetric and odd-symmetric receptive fields. Pooling of outputs from oppositely polarized simple cells leads to complex cells that respond to both contrast polarities. A neural network model is described which simulates how simple and complex cells self-organize starting from unsegregated and unoriented geniculocortical inputs during prenatal development. Neighboring simple cells that are sensitive to opposite contrast polarities develop from a combination of spatially short-range inhibition and high-gain recurrent habituative excitation between cells that obey membrane equations. Habituation, or depression, of synapses controls reset of cell activations both through enhanced ON responses and OFF antagonistic rebounds. Orientation and ocular dominance maps form when high-gain medium-range recurrent excitation and long-range inhibition interact with the short-range mechanisms. The resulting structure clarifies how simple and complex cells contribute to perceptual processes such as texture segregation and perceptual grouping.Air Force Office of Scientific Research (F49620-92-J-0334); British Petroleum (BP 89A-1204); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-4100); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409