We study the $p$-generalized probit regression model, which is a generalized linear model for binary responses. It extends the standard probit model by replacing its link function, the standard normal cdf, by a $p$-generalized normal distribution for $p\in[1, \infty)$. The $p$-generalized normal distributions \citep{Sub23} are of special interest in statistical modeling because they fit much more flexibly to data. Their tail behavior can be controlled by choice of the parameter $p$, which influences the model's sensitivity to outliers. Special cases include the Laplace, the Gaussian, and the uniform distributions. We further show how the maximum likelihood estimator for $p$-generalized probit regression can be approximated efficiently up to a factor of $(1+\varepsilon)$ on large data by combining sketching techniques with importance subsampling to obtain a small data summary called coreset.

The right to be forgotten has been legislated in many countries, but its enforcement in the AI industry would cause unbearable costs. When single data deletion requests come, companies may need to delete the whole models learned with massive resources. Existing works propose methods to remove knowledge learned from data for explicitly parameterized models, which however are not appliable to the sampling-based Bayesian inference, i.e., Markov chain Monte Carlo (MCMC), as MCMC can only infer implicit distributions. In this paper, we propose the first machine unlearning algorithm for MCMC. We first convert the MCMC unlearning problem into an explicit optimization problem. Based on this problem conversion, an MCMC influence function is designed to provably characterize the learned knowledge from data, which then delivers the MCMC unlearning algorithm. Theoretical analysis shows that MCMC unlearning would not compromise the generalizability of the MCMC models. Experiments on Gaussian mixture models and Bayesian neural networks confirm the effectiveness of the proposed algorithm. "The right to be forgotten" refers to the right of individuals to request data controllers such as tech giants to delete the data collected from them. It has been recognized in many countries through legislation, including the European Union's General Data Protection Regulation (2016) and the California Consumer Privacy Act (2018).

Energy-based latent variable models (EBLVMs) are more expressive than conventional energy-based models. However, its potential on visual tasks are limited by its training process based on maximum likelihood estimate that requires sampling from two intractable distributions. In this paper, we propose Bi-level doubly variational learning (BiDVL), which is based on a new bi-level optimization framework and two tractable variational distributions to facilitate learning EBLVMs. Particularly, we lead a decoupled EBLVM consisting of a marginal energy-based distribution and a structural posterior to handle the difficulties when learning deep EBLVMs on images. By choosing a symmetric KL divergence in the lower level of our framework, a compact BiDVL for visual tasks can be obtained. Our model achieves impressive image generation performance over related works. It also demonstrates the significant capacity of testing image reconstruction and out-of-distribution detection.

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?"

The Fokker-Planck (FP) equations, which describe the time evolution of probability density functions (PDFs) of complex stochastic systems, have been widely used in different fields such as physical and biological modelling[31][34]. Solving the FP equations numerically has been an important research topic in the past few decades. Generally, there are two main ways to obtain the PDFs of stochastic dynamics: solving the FP equations directly, or evaluating the transition probability density of the associated stochastic differential equations(SDEs). Traditional numerical methods for doing this include the finite element methods [4], the finite difference methods [19], the path integral methods [37], to name just a few. One of the biggest difficulties of these approaches is that either discretizition of a high dimensional (unbounded) physical space is needed, or a large number of sample paths via Monte Carlo method [12] should be used. In recent years, machine learning techniques have been widely used to solve partial differential equations (PDEs), see e.g.

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.