Cheating with Models

Beliefs and decisions are often based on confronting models with data. What is the largest “fake” correlation that a misspecified model can generate, even when it passes an elementary misspecification test? We study an “analyst” who fits a model, represented by a directed acyclic graph, to an objective (multivariate) Gaussian distribution. We characterize the maximal estimated pairwise correlation for generic Gaussian objective distributions, subject to the constraint that the estimated model preserves the marginal distribution of any individual variable. As the number of model variables grows, the estimated correlation can become arbitrarily close to one regardless of the objective correlation. (JEL D83, C13, C46, C51)

Multidimensional Dominance Drawings and Their Applications

In a dominance drawing Γ of a directed acyclic graph (DAG) G, a vertex v is reachable from a vertex u if, and only if all the coordinates of v are greater than or equal to the coordinates of u in Γ. Dominance drawings of DAGs are very important in many areas of research. They combine the aspect of drawing a DAG on the grid with the fact that the transitive closure of the DAG is apparently obvious by the dominance relation between grid points associated with the vertices. The smallest number d for which a given DAG G has a d-dimensional dominance drawing is called dominance drawing dimension, and it is NP-hard to compute. In this paper, we present efficient algorithms for computing dominance drawings of G with a number of dimensions respecting theoretical bounds. We first describe a simple algorithm that shows how to compute a dominance drawing of G from its compressed transitive closure. Next, we describe a more complicated algorithm, which is based on the concept of modular decomposition of G, and obtaining dominance drawings with a lower number of dimensions. Finally, we consider the concept of weak dominance, a relaxed version of the dominance, and we discuss interesting experimental results.

Lower bound for the spectral radius of the starlike trees

A tree is a connected acyclic graph. A tree is called a starlike if exactly one of its vertices has degree greater than two. Let λι be the largest eigenvalue of the adjacency matrix of a starlike tree. In this work, we obtain a lower bound for the spectral radius of a starlike tree. This bound only depends of the maximum degree of the vertices.

Performance Analysis of the IOTA DAG-Based Distributed Ledger

Distributed ledgers (DLs) provide many advantages over centralized solutions in Internet of Things projects, including but not limited to improved security, transparency, and fault tolerance. To leverage DLs at scale, their well-known limitation (i.e., performance) should be adequately analyzed and addressed. Directed acyclic graph-based DLs have been proposed to tackle the performance and scalability issues by design. The first among them, IOTA, has shown promising signs in addressing the preceding issues. IOTA is an open source DL designed for the Internet of Things. It uses a directed acyclic graph to store transactions on its ledger, to achieve a potentially higher scalability over blockchain-based DLs. However, due to the uncertainty and centralization of the deployed consensus, the current IOTA implementation exposes some performance issues, making it less performant than the initial design. In this article, we first extend an existing simulator to support realistic IOTA simulations and investigate the impact of different design parameters on IOTA’s performance. Then, we propose a layered model to help the users of IOTA determine the optimal waiting time to resend the previously submitted but not yet confirmed transaction. Our findings reveal the impact of the transaction arrival rate, tip selection algorithms, weighted tip selection algorithm randomness, and network delay on the throughput. Using the proposed layered model, we shed some light on the distribution of the confirmed transactions. The distribution is leveraged to calculate the optimal time for resending an unconfirmed transaction to the DL. The performance analysis results can be used by both system designers and users to support their decision making.

Ensemble Method of Convolutional Neural Networks with Directed Acyclic Graph Using Dermoscopic Images: Melanoma Detection Application

The early detection of melanoma is the most efficient way to reduce its mortality rate. Dermatologists achieve this task with the help of dermoscopy, a non-invasive tool allowing the visualization of patterns of skin lesions. Computer-aided diagnosis (CAD) systems developed on dermoscopic images are needed to assist dermatologists. These systems rely mainly on multiclass classification approaches. However, the multiclass classification of skin lesions by an automated system remains a challenging task. Decomposing a multiclass problem into a binary problem can reduce the complexity of the initial problem and increase the overall performance. This paper proposes a CAD system to classify dermoscopic images into three diagnosis classes: melanoma, nevi, and seborrheic keratosis. We introduce a novel ensemble scheme of convolutional neural networks (CNNs), inspired by decomposition and ensemble methods, to improve the performance of the CAD system. Unlike conventional ensemble methods, we use a directed acyclic graph to aggregate binary CNNs for the melanoma detection task. On the ISIC 2018 public dataset, our method achieves the best balanced accuracy (76.6%) among multiclass CNNs, an ensemble of multiclass CNNs with classical aggregation methods, and other related works. Our results reveal that the directed acyclic graph is a meaningful approach to develop a reliable and robust automated diagnosis system for the multiclass classification of dermoscopic images.