Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable. Sampling-based ABC algorithms such as rejection-and K2-ABC are inefficient when the parameters have high dimensions, while the regression-based algorithms such as K-and DR-ABC are hard to scale. In this paper, we introduce an optimization-based ABC framework that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed as saddle point problems, whose objectives can be accessed directly with samples. We present the predictive ABC algorithm (P-ABC), and provide a probabilistically approximately correct (PAC) bound that guarantees its learning consistency. Numerical experiment shows that P-ABC outperforms both K2-and DR-ABC significantly.

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Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable. Sampling-based ABC algorithms such as rejection-and K2-ABC are inefficient when the parameters have high dimensions, while the regression-based algorithms such as K-and DR-ABC are hard to scale. In this paper, we introduce an optimization-based ABC framework that addresses these deficiencies. Leveraging a generative model for posterior and joint distribution matching, we show that ABC can be framed as saddle point problems, whose objectives can be accessed directly with samples. We present the predictive ABC algorithm (P-ABC), and provide a probabilistically approximately correct (PAC) bound that guarantees its learning consistency. Numerical experiment shows that P-ABC outperforms both K2-and DR-ABC significantly.

Approximate Bayesian computation (ABC) is an important methodology for Bayesian inference when the likelihood function is intractable.

I am happy with all of your responses, though slightly confused over Q2 (rev2). One can't draw samples from improper priors in the first place, and other techniques (such as Rodrigues et al) won't save you there. You simply need to draw your samples from a distribution that is not the prior. I am still positively inclined towards this paper, and following the response and comparison to EP-ABC I will increase my score to 7 (from 6). Of course when the prior is improper or merely diffuse with respect to the posterior this will be impossible or at best highly inefficient.

Simulation based inference (SBI) methods enable the estimation of posterior distributions when the likelihood function is intractable, but where model simulation is feasible. Popular neural approaches to SBI are the neural posterior estimator (NPE) and its sequential version (SNPE). These methods can outperform statistical SBI approaches such as approximate Bayesian computation (ABC), particularly for relatively small numbers of model simulations. However, we show in this paper that the NPE methods are not guaranteed to be highly accurate, even on problems with low dimension. In such settings the posterior cannot be accurately trained over the prior predictive space, and even the sequential extension remains sub-optimal. To overcome this, we propose preconditioned NPE (PNPE) and its sequential version (PSNPE), which uses a short run of ABC to effectively eliminate regions of parameter space that produce large discrepancy between simulations and data and allow the posterior emulator to be more accurately trained. We present comprehensive empirical evidence that this melding of neural and statistical SBI methods improves performance over a range of examples, including a motivating example involving a complex agent-based model applied to real tumour growth data.

The utilization of existing terrestrial infrastructures to provide coverage for aerial users is a potentially low-cost solution. However, the already deployed terrestrial base stations (TBSs) result in weak ground-to-air (G2A) coverage due to the down-tilted antennas. Furthermore, achieving optimal coverage across the entire airspace through antenna adjustment is challenging due to the complex signal coverage requirements in three-dimensional space, especially in the vertical direction. In this paper, we propose a cooperative tri-point (CoTP) model-based method that utilizes cooperative beams to enhance the G2A coverage extension. To utilize existing TBSs for establishing effective cooperation, we prove that the cooperation among three TBSs can ensure G2A coverage with a minimum coverage overlap, and design the CoTP model to analyze the G2A coverage extension. Using the model, a cooperative coverage structure based on Delaunay triangulation is designed to divide triangular prism-shaped subspaces and corresponding TBS cooperation sets. To enable TBSs in the cooperation set to cover different height subspaces while maintaining ground coverage, we design a cooperative beam generation algorithm to maximize the coverage in the triangular prism-shaped airspace. The simulation results and field trials demonstrate that the proposed method can efficiently enhance the G2A coverage extension while guaranteeing ground coverage.

Answer selection (AS) is a critical subtask of the open-domain question answering (QA) problem. The present paper proposes a method called RLAS-BIABC for AS, which is established on attention mechanism-based long short-term memory (LSTM) and the bidirectional encoder representations from transformers (BERT) word embedding, enriched by an improved artificial bee colony (ABC) algorithm for pretraining and a reinforcement learning-based algorithm for training backpropagation (BP) algorithm. BERT can be comprised in downstream work and fine-tuned as a united task-specific architecture, and the pretrained BERT model can grab different linguistic effects. Existing algorithms typically train the AS model with positive-negative pairs for a two-class classifier. A positive pair contains a question and a genuine answer, while a negative one includes a question and a fake answer. The output should be one for positive and zero for negative pairs. Typically, negative pairs are more than positive, leading to an imbalanced classification that drastically reduces system performance. To deal with it, we define classification as a sequential decision-making process in which the agent takes a sample at each step and classifies it. For each classification operation, the agent receives a reward, in which the prize of the majority class is less than the reward of the minority class. Ultimately, the agent finds the optimal value for the policy weights. We initialize the policy weights with the improved ABC algorithm. The initial value technique can prevent problems such as getting stuck in the local optimum. Although ABC serves well in most tasks, there is still a weakness in the ABC algorithm that disregards the fitness of related pairs of individuals in discovering a neighboring food source position.

Fifteen Puzzle problem is one of the most classical problems that have captivated mathematical enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 1013 states that have to be explored and several algorithms have been applied to solve the Fifteen Puzzle instances. In this paper, to deal with this large state space, Bidirectional A* (BA*) search algorithm with three heuristics, such as Manhattan distance (MD), linear conflict (LC), and walking distance (WD) has been used to solve the Fifteen Puzzle problems. The three mentioned heuristics will be hybridized in a way that can dramatically reduce the number of generated states by the algorithm. Moreover, all those heuristics require only 25KB of storage but help the algorithm effectively reduce the number of generated states and expand fewer nodes. Our implementation of BA* search can significantly reduce the space complexity, and guarantee either optimal or near-optimal solutions.1

Artificial Bee Colony Algorithm (ABC) is an optimization algorithm based on the intelligent foraging behavior of a honey bee swarm. We'll be looking at the ABC algorithm in detail through its purpose, implementation, and functionality. We will then solve a few problems optimizing benchmark functions such as Sphere, Himmelblau, and the Cross-In-Tray function shown below. We will also look at the application of the ABC Algorithm to real-world business problems. Full, reusable code for the implementation is available on Github. At AAXIS Digital, we routinely encounter intractable business optimization problems that require out-of-the-box thinking. To model these business problems to be solved computationally, we need to model it as a list of decision variables representing a candidate solution and be able to compute a "measure of goodness", called the objective function.