Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued functions. Motivated by applications in human psychophysics where common experimental designs produce binary responses, we study LSE active sampling with Bernoulli outcomes. With Gaussian process classification surrogate models, the look-ahead model posteriors used by state-of-the-art continuous-output methods are intractable. However, we derive analytic expressions for look-ahead posteriors of sublevel set membership, and show how these lead to analytic expressions for a class of look-ahead LSE acquisition functions, including information-based methods. Benchmark experiments show the importance of considering the global look-ahead impact on the entire posterior. We demonstrate a clear benefit to using this new class of acquisition functions on benchmark problems, and on a challenging real-world task of estimating a high-dimensional contrast sensitivity function.

We propose a new differentiable probabilistic model over DAGs (DP-DAG). DP-DAG allows fast and differentiable DAG sampling suited to continuous optimization. To this end, DP-DAG samples a DAG by successively (1) sampling a linear ordering of the node and (2) sampling edges consistent with the sampled linear ordering. We further propose VI-DP-DAG, a new method for DAG learning from observational data which combines DP-DAG with variational inference. Hence, VI-DP-DAG approximates the posterior probability over DAG edges given the observed data. VI-DP-DAG is guaranteed to output a valid DAG at any time during training and does not require any complex augmented Lagrangian optimization scheme in contrast to existing differentiable DAG learning approaches. In our extensive experiments, we compare VI-DP-DAG to other differentiable DAG learning baselines on synthetic and real datasets. VI-DP-DAG significantly improves DAG structure and causal mechanism learning while training faster than competitors. Directed Acyclic Graphs (DAGs) are important mathematical objects in many machine learning tasks. For example, a direct application of DAGs is to represent causal relationships in a system of variables. In this case, variables are represented as nodes and causal relationships are represented as directed edges. Hence, DAG learning has found many applications for causal discovery in biology, economics or planning (Pearl, 1988; Ramsey et al., 2017; Sachs et al., 2005; Zhang et al., 2013). However, DAG learning is a challenging problem for two reasons. First, while DAG learning with data from randomized and controlled experiments is the gold-standard for causal discovery, experimental data might be hard or unethical to obtain in practice.

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for the data. However, this framework relies on the calculation of likelihood functions which are intractable for most models used in practice. Previous approaches in the field of Approximate Bayesian Computation (ABC) circumvent the evaluation of the likelihood and estimate the model evidence based on rejection sampling, but they are typically computationally intense. Here, I propose a new efficient method to perform Bayesian model comparison in ABC. Based on recent advances in posterior density estimation, the method approximates the posterior over models in parametric form. In particular, I train a mixture-density network to map features of the observed data to the posterior probability of the models. The performance is assessed with two examples. On a tractable model comparison problem, the underlying exact posterior probabilities are predicted accurately. In a use-case scenario from computational neuroscience -- the comparison between two ion channel models -- the underlying ground-truth model is reliably assigned a high posterior probability. Overall, the method provides a new efficient way to perform Bayesian model comparison on complex biophysical models independent of the model architecture.

This article is part of our coverage of the latest in AI research. Artificial intelligence research has made great achievements in solving specific applications, but we're still far from the kind of general-purpose AI systems that scientists have been dreaming of for decades. Among the solutions being explored to overcome the barriers of AI is the idea of neuro-symbolic systems that bring together the best of different branches of computer science. In a talk at the IBM Neuro-Symbolic AI Workshop, Joshua Tenenbaum, professor of computational cognitive science at the Massachusetts Institute of Technology, explained how neuro-symbolic systems can help to address some of the key problems of current AI systems. Among the many gaps in AI, Tenenbaum is focused on one in particular: "How do we go beyond the idea of intelligence as recognizing patterns in data and approximating functions and more toward the idea of all the things the human mind does when you're modeling the world, explaining and understanding the things you're seeing, imagining things that you can't see but could happen, and making them into goals that you can achieve by planning actions and solving problems?"

In this paper, an online task scheduling and mapping method based on a fuzzy neural network (FNN) learned by an evolutionary multi-objective algorithm (NSGA-II) to jointly optimize the main design challenges of heterogeneous MPSoCs is proposed. In this approach, first, the FNN parameters are trained using an NSGA-II-based optimization engine by considering the main design challenges of MPSoCs including temperature, power consumption, failure rate, and execution time on a training dataset consisting of different application graphs of various sizes. Next, the trained FNN is employed as an online task scheduler to jointly optimize the main design challenges in heterogeneous MPSoCs. Due to the uncertainty in sensor measurements and the difference between computational models and reality, applying the fuzzy neural network is advantageous in online scheduling procedures. The performance of the method is compared with some previous heuristic, meta-heuristic, and rule-based approaches in several experiments. Based on these experiments our proposed method outperforms the related studies in optimizing all design criteria. Its improvement over related heuristic and meta-heuristic approaches are estimated 10.58% in temperature, 9.22% in power consumption, 39.14% in failure rate, and 12.06% in execution time, averagely. Moreover, considering the interpretable nature of the FNN, the frequently fired extracted fuzzy rules of the proposed approach are demonstrated.

State-of-the-art spectral energy distribution (SED) analyses use a Bayesian framework to infer the physical properties of galaxies from observed photometry or spectra. They require sampling from a high-dimensional space of SED model parameters and take $>10-100$ CPU hours per galaxy, which renders them practically infeasible for analyzing the $billions$ of galaxies that will be observed by upcoming galaxy surveys ($e.g.$ DESI, PFS, Rubin, Webb, and Roman). In this work, we present an alternative scalable approach to rigorous Bayesian inference using Amortized Neural Posterior Estimation (ANPE). ANPE is a simulation-based inference method that employs neural networks to estimate the posterior probability distribution over the full range of observations. Once trained, it requires no additional model evaluations to estimate the posterior. We present, and publicly release, ${\rm SED}{flow}$, an ANPE method to produce posteriors of the recent Hahn et al. (2022) SED model from optical photometry. ${\rm SED}{flow}$ takes ${\sim}1$ $second~per~galaxy$ to obtain the posterior distributions of 12 model parameters, all of which are in excellent agreement with traditional Markov Chain Monte Carlo sampling results. We also apply ${\rm SED}{flow}$ to 33,884 galaxies in the NASA-Sloan Atlas and publicly release their posteriors: see https://changhoonhahn.github.io/SEDflow.

Given a supervised machine learning problem where the training set has been subject to a known sampling bias, how can a model be trained to fit the original dataset? We achieve this through the Bayesian inference framework by altering the posterior distribution to account for the sampling function. We then apply this solution to binary logistic regression, and discuss scenarios where a dataset might be subject to intentional sample bias such as label imbalance. This technique is widely applicable for statistical inference on big data, from the medical sciences to image recognition to marketing. Familiarity with it will give the practitioner tools to improve their inference pipeline from data collection to model selection.

Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization, following noisy estimates of the natural gradient. However, almost all the state-of-the-art SVI algorithms are based on first-order optimization algorithm and often suffer from poor convergence rate. In this paper, we bridge the gap between second-order methods and stochastic variational inference by proposing a second-order based stochastic variational inference approach. In particular, firstly we derive the Hessian matrix of the variational objective. Then we devise two numerical schemes to implement second-order SVI efficiently. Thorough empirical evaluations are investigated on both synthetic and real dataset to backup both the effectiveness and efficiency of the proposed approach.

Artificial intelligence (AI) and machine learning models are being increasingly deployed in real-world applications.

Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate inference techniques can be used to handle the statistical approximations principled and practically by framing the control problem as a problem of input estimation. Analyzing the Gaussian setting, we present an inference-based solver that is effective in stochastic and deterministic settings and was found to be superior to popular baselines on nonlinear simulated tasks. We draw connections that relate this inference formulation to previous approaches for stochastic optimal control and outline several advantages that this inference view brings due to its statistical nature.