Cost-sensitive label embedding for multi-label classification

This paper presents a Bayesian approach for the optimal control of a machine that can experience setup errors assuming an asymmetric off-target cost function. It is assumed that the setup error cannot be observed directly due to presence of measurement and part-to-part errors, and it is further assumed that the variance of this error is not known a priori. The setup error can be compensated by performing sequential adjustments of the process mean based on observations of the parts produced. It is shown how the proposed method converges to the optimal (known variance) trajectory, recovering from a possibly biased initial variance estimate. Simulations results are presented to show the small sample behavior of the proposed method under two types of asymmetric off-target cost functions: a constant asymmetric and a quadratic asymmetric cost function.

By deriving an upper bound of the so-called 'price of anarchy', this paper analyses the efficiency of oligopolistic games in networks with non-separable and asymmetric cost functions, splittable flows and fixed demands. The new bound is determined by the optimal objective function values of some optimisation problems. In particular, for some special cases, the bound turns out to be explicit in the sense that it is representable explicitly by the number of players, and the constants measuring the degree of asymmetry and non-linearity of the cost function. Copyright © 2010 Inderscience Enterprises Ltd.

This study investigates game-based PIMFY models for analyzing the interactions among grant-seeking local governments and the central government. From these models we could find the following. The effective prize dissipation ratio in each local government multiplied by its population is the same in two competing local governments – in the first case, of equal valuation and equal cost functions, and in the second case, of equal valuation and asymmetric cost functions. If the central government uses a policy to strengthen cost advantage in favor of the low cost local government, then economic inefficiency in terms of aggregate outlays will decrease. If there a binding constraint on outlay by local government 1 is assigned by the central government, then at the binding level of outlay, local government 2’s new equilibrium level needs to be calculated and it will be smaller than the equilibrium level without the binding constraint.

A modelling approach for solving quite general network equilibrium problems (with fixed trip productions and attractions) intrinsic to the urban transport planning process is presented. The framework can consider a variety of demand models and route choice behaviours within the same implementation, including multiple user classes and combined travel modes that interact on the same physical network. The demand choices are assumed to have a hierarchical structure. When trip distribution is variable, a doubly constrained entropy‐maximizing model is considered at the first level of choice and a hierarchical logit model is used for the remaining demand choices (time of departure, travel mode, transfer point for combined modes, etc.). If trip distribution is considered to be exogenous, the demand choices are modelled as a hierarchical logit. One of the main features of the model is that it considers the effects of congestion on the road network as well as congestion and capacity constraints effects in each public transport service network. The problem is formulated mathematically as a variational inequality, with asymmetric cost functions, and solved following the diagonalization procedure. Each iteration of the aforementioned procedure solves an optimization problem using the Evans algorithm. Sufficient conditions for the existence and uniqueness of the solution to the diagonalized problem are obtained. The main results of a simple example (solved with an academic version of the proposed algorithm) are presented to show the consistency of the equilibrium flows and levels of services obtained using the model. Finally, a real scale implementation of the model is briefly described to show the feasibility of its application.

This paper is a study of a genetic adaptive scheme design for L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -gain state feedback controllers. It is known that the design of the initial gain producer of the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -gain state feedback controller (LC) is a difficult problem. The derivative-free optimization, the genetic algorithm, is utilized to resolve the high initial gain problem of LC for a class of nonlinear systems. It is a novel approach for robust control and can be considered as a special application of genetic algorithms. A real-value genetic algorithm with on-line characteristics is designed to search a suitable control gain of LC under auxiliary searching conditions and a specific cost function. The specific cost function is designed under Lyapunov stable theory. Since the system has the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -gain control properties, then the system states are bounded in an assignable region so that the stability of the initial system is guaranteed. Thus, the system stability of any searched results is guaranteed. Besides, due to the assignable L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -gain attenuation level, the search space of the genetic algorithm is definable. The search target of the genetic algorithm is to find a suitable set of the initial gain so that the system can have required initial control performance. The simulation results indeed demonstrate the effectiveness of the proposed approach.

Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function, or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single-parameter or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement. Published by the American Physical Society 2024

Multidimensional scaling (MDS) is a technique for visualizing multidimensional data points as a 2D scatter plot. It can be applied to execution profiles of software to reveal how similar executions are to one another. This is useful for certain software engineering applications, which require accurate representation of small dissimilarities and nearest neighbor relationships. However, the high-dimensionality of profiles can cause MDS techniques to represent small dissimilarities poorly. We evaluate several variants of MDS on large sets of profiles, to see which techniques produce the most accurate displays. These include four previously proposed techniques -classical scaling followed by iterative majorization, energy minimization, ordinal AIDS, and cluster differences scaling - and two techniques of our invention - hierarchical MDS and sparse region scaling. The results suggest that each technique except ordinal MDS can significantly improve the representation of small dissimilarities between program executions and that hierarchical MDS and sparse region scaling perform best overall

We introduce a combinatorial variant of the cost sharing problem: several services can be provided to each player and each player values every combination of services differently. A publicly known cost function specifies the cost of providing every possible combination of services. A combinatorial cost sharing mechanism is a protocol that decides which services each player gets and at what price. We look for dominant strategy mechanisms that are (economically) efficient and cover the cost, ideally without overcharging (i.e., budget balanced). Note that unlike the standard cost sharing setting, combinatorial cost sharing is a multi-parameter domain. This makes designing dominant strategy mechanisms with good guarantees a challenging task. We present the Potential Mechanism -- a combination of the VCG mechanism and a well-known tool from the theory of cooperative games: Hart and Mas-Colell's potential function. The potential mechanism is a dominant strategy mechanism that always covers the incurred cost. When the cost function is subadditive the same mechanism is also approximately efficient. Our main technical contribution shows that when the cost function is submodular the potential mechanism is approximately budget balanced in three settings: supermodular valuations, symmetric cost function and general symmetric valuations, and two players with general valuations.

Application of a Long Short Term Memory neural predictor with asymmetric loss function for the resource allocation in NFV network architectures

The high time needed to reconfigure cloud resources in Network Function Virtualization network environments has led to the proposal of solutions in which a prediction based-resource allocation is performed. All of them are based on traffic or needed resource prediction with the minimization of symmetric loss functions like Mean Squared Error. When inevitable prediction errors are made, the prediction methodologies are not able to differently weigh positive and negative prediction errors that could impact the total network cost. In fact if the predicted traffic is higher than the real one then an over allocation cost, referred to as over-provisioning cost, will be paid by the network operator; conversely, in the opposite case, Quality of Service degradation cost, referred to as under-provisioning cost, will be due to compensate the users because of the resource under allocation. In this paper we propose and investigate a resource allocation strategy based on a Long Short Term Memory algorithm in which the training operation is based on the minimization of an asymmetric cost function that differently weighs the positive and negative prediction errors and the corresponding over-provisioning and under-provisioning costs. In a typical traffic and network scenario, the proposed solution allows for a cost saving by 30% with respect to the case of solution with symmetric cost function.

In this chapter, we present the classic approach to calculate and decompose cost and revenue efficiency based on Shephard’s radial input and output distance functions. These decompositions follow closely the presentation done in Chap. 2 where both economic efficiency measures can be separated into technical and allocative components, i.e., expressions (2.33) and (2.44). However, rather than resorting to Farrell’s input and output technical efficiency measures, the decomposition is formalized in terms of the distance function and duality theory. At the time of publishing his seminal paper in 1957, Farrell did not seem to be aware of the work by Shephard, printed initially in his 1953 book titled Theory of Cost and Production Functions. There, he formalized the duality between the cost function and the input distance function, constituting the theoretical base for the decomposition of economic efficiency. Farrell cites Debreu’s (1951) “coefficient of resource utilization” as a source of inspiration, although, had he been aware of it, he could have relied equally on Shephard’s contribution, which is specific to production theory. Nevertheless, Shephard never introduced the concept of overall economic efficiency nor that of allocative efficiency, being one step short of proposing this decomposition explicitly.

Humans still outperform robots in most manipulation and locomotion tasks. Research suggests that humans minimize a task specific cost function when performing movements. In this paper we present a Gaussian Process based method to learn the underlying cost function, without making assumptions on its structure, and reproduce the demonstrated movement on a robot using a linear model predictive control framework. We show that the learned cost function can be used to prioritize between tracking and additional cost functions based on exemplar variance, and satisfy task and joint space constraints. Tuning the weighting between learned position and velocity costs produces trajectories of the desired shape even in the presence of constraints. The approach is validated in simulation with a simple 2dof manipulator showing joint and task space tracking and with a 4dof manipulator reproducing trajectories based on a human handwriting dataset.

A traffic system can be interpreted as a multiagent system, wherein vehicles choose the most efficient driving approaches guided by interconnected goals or strategies. This paper aims to develop a family of mean field games (MFG) for generic second-order traffic flow models (GSOM), in which cars control individual velocity to optimize their objective functions. GSOMs do not generally assume that cars optimize self-interested objectives, so such a game-theoretic reinterpretation offers insights into the agents’ underlying behaviors. In general, an MFG allows one to model individuals on a microscopic level as rational utility-optimizing agents while translating rich microscopic behaviors to macroscopic models. Building on the MFG framework, we devise a new class of second-order traffic flow MFGs (i.e., GSOM-MFG), which control cars’ acceleration to ensure smooth velocity change. A fixed-point algorithm with fictitious play technique is developed to solve GSOM-MFG numerically. In numerical examples, different traffic patterns are presented under different cost functions. For real-world validation, we further use an inverse reinforcement learning approach (IRL) to uncover the underlying cost function on the next-generation simulation (NGSIM) data set. We formulate the problem of inferring cost functions as a min-max game and use an apprenticeship learning algorithm to solve for cost function coefficients. The results show that our proposed GSOM-MFG is a generic framework that can accommodate various cost functions. The Aw Rascle and Zhang (ARZ) and Light-Whitham-Richards (LWR) fundamental diagrams in traffic flow models belong to our GSOM-MFG when costs are specified. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: X. Di is supported by the National Science Foundation [CAREER Award CMMI-1943998]. E. Iacomini is partially supported by the Italian Research Center on High-Performance Computing, Big Data and Quantum Computing (ICSC) funded by MUR Missione 4-Next Generation EU (NGEU) [Spoke 1 “FutureHPC &amp; BigData”]. C. Segala and M. Herty thank the Deutsche Forschungsgemeinschaft (DFG) for financial support [Grants 320021702/GRK2326, 333849990/IRTG-2379, B04, B05, and B06 of 442047500/SFB1481, HE5386/18-1,19-2,22-1,23-1,25-1, ERS SFDdM035; Germany’s Excellence Strategy EXC-2023 Internet of Production 390621612; and Excellence Strategy of the Federal Government and the Länder]. Support through the EU DATAHYKING is also acknowledged. This work was also funded by the DFG [TRR 154, Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks, Projects C03 and C05, Project No. 239904186]. Moreover, E. Iacomini and C. Segala are members of the Indam GNCS (Italian National Group of Scientific Calculus).

With shortest-path distances as input, classical multidimensional scaling can be regarded as a spectral graph drawing algorithm, and recent approximation techniques make it scale to very large graphs. In comparison with other methods, however, it is considered inflexible and prone to degenerate layouts for some classes of graphs. We want to challenge this belief by demonstrating that the method can be flexibly adapted to provide focus+context layouts. Moreover, we propose an alternative instantiation that appears to be more suitable for graph drawing and prevents certain degeneracies.

ABSTRACTThis paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney–Kadane and Metropolis–Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring.