Global Likelihood Function Research Articles

A novel Bayesian federated learning framework to address multi-dimensional heterogeneity problem

<abstract><p>Federated learning (FL) has attracted a lot of interests as a promising machine learning approach to protect user privacy and data security. It requires the clients to send model parameters to the server rather than private datasets, thus protecting privacy to a significant extent. However, there are several types of heterogeneities (data, model, objective and systems) in FL scenario, posing distinct challenges to the canonical FL algorithm (FedAvg). In this work, we propose a novel FL framework that integrates knowledge distillation and Bayesian inference to address this multi-dimensional heterogeneity problem. On the client side, we approximate the local likelihood function using a scaled multi-dimensional Gaussian probability density function (PDF). Moreover, each client is allowed to design customized model according to the requirement through knowledge distillation. On the server side, a multi-Gaussian product mechanism is employed to construct and maximize the global likelihood function, greatly enhancing the accuracy of the aggregated model in the case of data heterogeneity. Finally, we show in extensive empirical experiments on various datasets and settings that global model and local model can achieve better performance and require fewer communication rounds to converge compared with other FL techniques.</p></abstract>

Bayesian updating for data adjustments and multi-level uncertainty propagation within Total Monte Carlo

In this work, a method is proposed for combining differential and integral benchmark experimental data within a Bayesian framework for nuclear data adjustments and multi-level uncertainty propagation, using the Total Monte Carlo method. First, input parameters to basic nuclear physics models implemented within the TALYS code, were randomly varied to produce a large set of random nuclear data files. Next, a probabilistic data assimilation was carried out by computing the likelihood function for each random nuclear data file based first on only differential experimental data and then on integral benchmark data. The individual likelihood functions from the two updates were then combined into a global likelihood function. The proposed method was applied for the adjustment of n+208Pb in the fast energy region below 20 MeV. The adjusted file was compared with available experimental data as well as evaluations from the major nuclear data libraries and found to compare favourably.

A global likelihood for precision constraints and flavour anomalies

We present a global likelihood function in the space of dimension-six Wilson coefficients in the Standard Model Effective Field Theory. The likelihood includes contributions from flavour-changing neutral current B decays, lepton flavour universality tests in charged- and neutral-current B and K decays, meson-antimeson mixing observables in the K, B, and D systems, direct CP violation in Krightarrow pi pi , charged lepton flavour violating B, tau, and muon decays, electroweak precision tests on the Z and W poles, the anomalous magnetic moments of the electron, muon, and tau, and several other precision observables, 265 in total. The Wilson coefficients can be specified at any scale, with the one-loop running above and below the electroweak scale automatically taken care of. The implementation of the likelihood function is based on the open source tools flavio and wilson as well as the open Wilson coefficient exchange format (WCxf) and can be installed as a Python package. It can serve as a basis either for model-independent fits or for testing dynamical models, in particular models built to address the anomalies in B physics. We discuss a number of example applications, reproducing results from the EFT and model building literature.

An Efficient Likelihood-Based Modulation Classification Algorithm for Multiple-Input Multiple-Output Systems

Blind algorithms for multiple-input multiple-output (MIMO) signals interception have recently received considerable attention because of their important applications in modern civil and military communication fields. One key step in the interception process is to blindly recognize the modulation type of the MIMO signals. This can be performed by employing a Modulation Classification (MC) algorithm, which can be feature-based or likelihood-based. To overcome the problems associated with the existing likelihood-based MC algorithms, a new algorithm is developed in this paper. We formulated the MC problem as maximizing a global likelihood function formed by combining the likelihood functions for the estimated transmitted signals, where Minimum Mean Square Error (MMSE) filtering is employed to separate the MIMO channel into several sub-channels. Simulation results showed that the proposed algorithm works well under various operating conditions, and performs close to the performance upper bound with reasonable complexity.

Distributed Particle Filter for Target Tracking: With Reduced Sensor Communications

For efficient and accurate estimation of the location of objects, a network of sensors can be used to detect and track targets in a distributed manner. In nonlinear and/or non-Gaussian dynamic models, distributed particle filtering methods are commonly applied to develop target tracking algorithms. An important consideration in developing a distributed particle filtering algorithm in wireless sensor networks is reducing the size of data exchanged among the sensors because of power and bandwidth constraints. In this paper, we propose a distributed particle filtering algorithm with the objective of reducing the overhead data that is communicated among the sensors. In our algorithm, the sensors exchange information to collaboratively compute the global likelihood function that encompasses the contribution of the measurements towards building the global posterior density of the unknown location parameters. Each sensor, using its own measurement, computes its local likelihood function and approximates it using a Gaussian function. The sensors then propagate only the mean and the covariance of their approximated likelihood functions to other sensors, reducing the communication overhead. The global likelihood function is computed collaboratively from the parameters of the local likelihood functions using an average consensus filter or a forward-backward propagation information exchange strategy.

Error Propagation in Gossip-Based Distributed Particle Filters

This paper examines the impact of the gossip procedure on distributed particle filters that employ averaging to estimate the global likelihood function. We consider a model where a gossip-driven algorithm leads to the use of a slightly distorted version of the likelihood function, in lieu of its true value. Under standard regularity conditions, and a mild assumption on the true likelihood function, we derive a time-uniform bound on the weak-sense $L_p$ error of the filter. Furthermore, we present an associated exponential inequality for the large deviations of the filter. These bounds capture the combined effects of sampling and consensus-based approximation. The results allow us to evaluate the impact of such approximations on the overall performance of the distributed particle filter, and analyze its stability. Finally, through numerical experiments, we demonstrate the practical implications of these results and explore the relationship of the performance of the filter with these theoretical error bounds.

Low‐Complexity Gaussian Detection for MIMO Systems

For single‐carrier transmission over delay‐spread multi‐input multi‐output (MIMO) channels, the computational complexity of the receiver is often considered as a bottleneck with respect to (w.r.t.) practical implementations. Multi‐antenna interference (MAI) together with intersymbol interference (ISI) provides fundamental challenges for efficient and reliable data detection. In this paper, we carry out a systematic study on the interference structure of MIMO‐ISI channels, and sequentially deduce three different Gaussian approximations to simplify the calculation of the global likelihood function. Using factor graphs as a general framework and applying the Gaussian approximation, three low‐complexity iterative detection algorithms are derived, and their performances are compared by means of Monte Carlo simulations. After a careful inspection of their merits and demerits, we propose a graph‐based iterative Gaussian detector (GIGD) for severely delay‐spread MIMO channels. The GIGD is characterized by a strictly linear computational complexity w.r.t. the effective channel memory length, the number of transmit antennas, and the number of receive antennas. When the channel has a sparse ISI structure, the complexity of the GIGD is strictly proportional to the number of nonzero channel taps. Finally, the GIGD provides a near‐optimum performance in terms of the bit error rate (BER) for repetition encoded MIMO systems.

Likelihood analysis of the constrained minimal supersymmetric standard model parameter space

We present a likelihood analysis of the parameter space of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), in which the input scalar masses m_0 and fermion masses m_{1/2} are each assumed to be universal. We include the full experimental likelihood function from the LEP Higgs search as well as the likelihood from a global precision electroweak fit. We also include the likelihoods for b to s gamma decay and (optionally) g_mu - 2. For each of these inputs, both the experimental and theoretical errors are treated. We include the systematic errors stemming from the uncertainties in m_t and m_b, which are important for delineating the allowed CMSSM parameter space as well as calculating the relic density of supersymmetric particles. We assume that these dominate the cold dark matter density, with a density in the range favoured by WMAP. We display the global likelihood function along cuts in the (m_{1/2}, m_0) planes for tan beta = 10 and both signs of mu, tan beta = 35, mu < 0 and tan beta = 50, mu > 0, which illustrate the relevance of g_mu - 2 and the uncertainty in m_t. We also display likelihood contours in the (m_{1/2}, m_0) planes for these values of tan beta. The likelihood function is generally larger for mu > 0 than for mu < 0, and smaller in the focus-point region than in the bulk and coannihilation regions, but none of these possibilities can yet be excluded.