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Analyzing the effect of business cycle on rating transitions has been a subject of great interest these last fifteen years, particularly due to the increasing pressure coming from regulators for stress testing. In this paper, we consider that the dynamics of rating migrations is governed by an unobserved latent factor. Under a point process filtering framework, we explain how the current state of the hidden factor can be efficiently inferred from observations of rating histories. We then adapt the classical Baum-Welsh algorithm to our setting and show how to estimate the latent factor parameters. Once calibrated, we may reveal and detect economic changes affecting the dynamics of rating migration, in real-time. To this end we adapt a filtering formula which can then be used for predicting future transition probabilities according to economic regimes without using any external covariates. We propose two filtering frameworks: a discrete and a continuous version. We demonstrate and compare the efficiency of both approaches on fictive data and on a corporate credit rating database. The methods could also be applied to retail credit loans.

Long ties, the social ties that bridge different communities, are widely believed to play crucial roles in spreading novel information in social networks. However, some existing network theories and prediction models indicate that long ties might dissolve quickly or eventually become redundant, thus putting into question the long-term value of long ties. Our empirical analysis of real-world dynamic networks shows that contrary to such reasoning, long ties are more likely to persist than other social ties, and that many of them constantly function as social bridges without being embedded in local networks. Using a novel cost-benefit analysis model combined with machine learning, we show that long ties are highly beneficial, which instinctively motivates people to expend extra effort to maintain them. This partly explains why long ties are more persistent than what has been suggested by many existing theories and models. Overall, our study suggests the need for social interventions that can promote the formation of long ties, such as mixing people with diverse backgrounds.

Predictive business process monitoring aims at providing predictions about running instances by analyzing logs of completed cases in a business process. Recently, a lot of research focuses on increasing productivity and efficiency in a business process by forecasting potential problems during its executions. However, most of the studies lack suggesting concrete actions to improve the process. They leave it up to the subjective judgment of a user. In this paper, we propose a novel method to connect the results from predictive business process monitoring to actual business process improvements. More in detail, we optimize the resource allocation in a non-clairvoyant online environment, where we have limited information required for scheduling, by exploiting the predictions. The proposed method integrates the offline prediction model construction that predicts the processing time and the next activity of an ongoing instance using Bayesian Neural Networks (BNNs) with the online resource allocation that is extended from the minimum cost and maximum flow algorithm. To validate the proposed method, we performed experiments using an artificial event log and a real-life event log from a global financial organization.

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of the optimal miss error probability -- as the sample size tends to infinity -- given some (positive) restrictions on the false alarm probabilities is a fundamental question to address in theory. Considering the more realistic context of a BHT with a finite number of observations, this paper presents a new non-asymptotic result for the scenario with monotonic (sub-exponential decreasing) restriction on the Type I error probability, which extends the result presented by Strassen in 2009. Building on the use of concentration inequalities, we offer new upper and lower bounds to the optimal Type II error probability for the case of finite observations. Finally, the derived bounds are evaluated and interpreted numerically (as a function of the number samples) for some vanishing Type I error restrictions.

In spite of its high practical relevance, cluster specific multiple inference for linear mixed model predictors has hardly been addressed so far. While marginal inference for population parameters is well understood, conditional inference for the cluster specific predictors is more intricate. This work introduces a general framework for multiple inference in linear mixed models for cluster specific predictors. Consistent confidence sets for multiple inference are constructed under both, the marginal and the conditional law. Furthermore, it is shown that, remarkably, corresponding multiple marginal confidence sets are also asymptotically valid for conditional inference. Those lend themselves for testing linear hypotheses using standard quantiles without the need of re-sampling techniques. All findings are validated in simulations and illustrated along a study on Covid-19 mortality in US state prisons.

A Gaussian process (GP)-based methodology is proposed to emulate computationally expensive dynamical computer models or simulators. The method relies on emulating the short-time numerical flow map of the model. The flow map returns the solution of a dynamic system at an arbitrary time for a given initial condition. The prediction of the flow map is performed via a GP whose kernel is estimated using random Fourier features. This gives a distribution over the flow map such that each realisation serves as an approximation to the flow map. A realisation is then employed in an iterative manner to perform one-step ahead predictions and forecast the whole time series. Repeating this procedure with multiple draws from the emulated flow map provides a probability distribution over the time series. The mean and variance of that distribution are used as the model output prediction and a measure of the associated uncertainty, respectively. The proposed method is used to emulate several dynamic non-linear simulators including the well-known Lorenz attractor and van der Pol oscillator. The results show that our approach has a high prediction performance in emulating such systems with an accurate representation of the prediction uncertainty.

The present study develops a physics-constrained neural network (PCNN) to predict sequential patterns and motions of multiphase flows (MPFs), which includes strong interactions among various fluid phases. To predict the order parameters, which locate individual phases, in the future time, the conditional neural processes and long short-term memory (CNP-LSTM) are applied to quickly infer the dynamics of the phases after encoding only a few observations. After that, the multiphase consistent and conservative boundedness mapping algorithm (MCBOM) is implemented to correct the order parameters predicted from CNP-LSTM in order to strictly satisfy the mass conservation, the summation of the volume fractions of the phases to be unity, the consistency of reduction, and the boundedness of the order parameters. Then, the density of the fluid mixture is updated from the corrected order parameters. Finally, the velocity in the future time is predicted by a physics-informed CNP-LSTM (PICNP-LSTM) where conservation of momentum is included in the loss function with the observed density and velocity as the inputs. The proposed PCNN for MPFs sequentially performs (CNP-LSTM)-(MCBOM)-(PICNP-LSTM), which avoids unphysical behaviors of the order parameters, accelerates the convergence, and requires fewer data to make predictions. Numerical experiments demonstrate that the proposed PCNN is capable of predicting MPFs effectively.

The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different periods. The resulting possible inter-epidemic variability is rarely explicitly considered. Here, we propose to tackle multiple epidemics through a unique model incorporating a stochastic representation for each epidemic and to jointly estimate its parameters from noisy and partial observations. By building on a previous work, a Gaussian state-space model is extended to a model with mixed effects on the parameters describing simultaneously several epidemics and their observation process. An appropriate inference method is developed, by coupling the SAEM algorithm with Kalman-type filtering. Its performances are investigated on SIR simulated data. Our method outperforms an inference method separately processing each dataset. An application to SEIR influenza outbreaks in France over several years using incidence data is also carried out, by proposing a new version of the filtering algorithm. Parameter estimations highlight a non-negligible variability between influenza seasons, both in transmission and case reporting. The main contribution of our study is to rigorously and explicitly account for the inter-epidemic variability between multiple outbreaks, both from the viewpoint of modeling and inference.

Time appears to pass irreversibly. In light of CPT symmetry, the Universe's initial condition is thought to be somehow responsible. We propose a model, the stochastic partitioned cellular automaton (SPCA), in which to study the mechanisms and consequences of emergent irreversibility. While their most natural definition is probabilistic, we show that SPCA dynamics can be made deterministic and reversible, by attaching randomly initialized degrees of freedom. This property motivates analogies to classical field theories. We develop the foundations of non-equilibrium statistical mechanics on SPCAs. Of particular interest are the second law of thermodynamics, and a mutual information law which proves fundamental in non-equilibrium settings. We believe that studying the dynamics of information on SPCAs will yield insights on foundational topics in computer engineering, the sciences, and the philosophy of mind. As evidence of this, we discuss several such applications, including an extension of Landauer's principle, and sketch a physical justification of the causal decision theory that underlies the so-called psychological arrow of time.

Machine learning methods are powerful in distinguishing different phases of matter in an automated way and provide a new perspective on the study of physical phenomena. We train a Restricted Boltzmann Machine (RBM) on data constructed with spin configurations sampled from the Ising Hamiltonian at different values of temperature and external magnetic field using Monte Carlo methods. From the trained machine we obtain the flow of iterative reconstruction of spin state configurations to faithfully reproduce the observables of the physical system. We find that the flow of the trained RBM approaches the spin configurations of the maximal possible specific heat which resemble the near criticality region of the Ising model. In the special case of the vanishing magnetic field the trained RBM converges to the critical point of the Renormalization Group (RG) flow of the lattice model. Our results suggest an alternative explanation of how the machine identifies the physical phase transitions, by recognizing certain properties of the configuration like the maximization of the specific heat, instead of associating directly the recognition procedure with the RG flow and its fixed points. Then from the reconstructed data we deduce the critical exponent associated to the magnetization to find satisfactory agreement with the actual physical value. We assume no prior knowledge about the criticality of the system and its Hamiltonian.