We consider the problem of learning the underlying graph of a sparse Ising model with $p$ nodes from $n$ i.i.d. samples. The most recent and best performing approaches combine an empirical loss (the logistic regression loss or the interaction screening loss) with a regularizer (an L1 penalty or an L1 constraint). This results in a convex problem that can be solved separately for each node of the graph. In this work, we leverage the cardinality constraint L0 norm, which is known to properly induce sparsity, and further combine it with an L2 norm to better model the non-zero coefficients. We show that our proposed estimators achieve an improved sample complexity, both (a) theoretically -- by reaching new state-of-the-art upper bounds for recovery guarantees -- and (b) empirically -- by showing sharper phase transitions between poor and full recovery for graph topologies studied in the literature -- when compared to their L1-based counterparts.

Probabilistic inference in pairwise Markov Random Fields (MRFs), i.e. computing the partition function or computing a MAP estimate of the variables, is a foundational problem in probabilistic graphical models. Semidefinite programming relaxations have long been a theoretically powerful tool for analyzing properties of probabilistic inference, but have not been practical owing to the high computational cost of typical solvers for solving the resulting SDPs. In this paper, we propose an efficient method for computing the partition function or MAP estimate in a pairwise MRF by instead exploiting a recently proposed coordinate-descent-based fast semidefinite solver. We also extend semidefinite relaxations from the typical binary MRF to the full multi-class setting, and develop a compact semidefinite relaxation that can again be solved efficiently using the solver. We show that the method substantially outperforms (both in terms of solution quality and speed) the existing state of the art in approximate inference, on benchmark problems drawn from previous work. We also show that our approach can scale to large MRF domains such as fully-connected pairwise CRF models used in computer vision.

Learning task-agnostic dynamics models in high-dimensional observation spaces can be challenging for model-based RL agents. We propose a novel way to learn latent world models by learning to predict sequences of future actions conditioned on task completion. These task-conditioned models adaptively focus modeling capacity on task-relevant dynamics, while simultaneously serving as an effective heuristic for planning with sparse rewards. We evaluate our method on challenging visual goal completion tasks and show a substantial increase in performance compared to prior model-free approaches. Deep reinforcement learning has proven to be a powerful and effective framework for solving a diversity of challenging decision-making problems (Silver et al., 2017a; Berner et al., 2019). However these algorithms are typically trained to maximize a single reward function, ignoring information that is not directly relevant to the associated task at hand. This way of learning is in stark contrast to how humans learn (Tenenbaum, 2018). Without being prompted by a specific task, humans can still explore their environment, practice achieving imaginary goals, and in so doing learn about the dynamics of the environment. When subsequently presented with a novel task, humans can utilize this learned knowledge to bootstrap learning -- a property we would like our artificial agents to have. In this work, we investigate one way to bridge this gap by learning world models (Ha & Schmidhuber, 2018) that enable the realization of previously unseen tasks. By modeling the task-agnostic dynamics of an environment, an agent can make predictions about how its own actions may affect the environment state without the need for additional samples from the environment. Prior work has shown that by using powerful function approximators to model environment dynamics, training an agent entirely within its own world models can result in large gains in sample efficiency (Ha & Schmidhuber, 2018).

We propose two generic methods for improving semi-supervised learning (SSL). The first integrates weight perturbation (WP) into existing "consistency regularization" (CR) based methods. We implement WP by leveraging variational Bayesian inference (VBI). The second method proposes a novel consistency loss called "maximum uncertainty regularization" (MUR). While most consistency losses act on perturbations in the vicinity of each data point, MUR actively searches for "virtual" points situated beyond this region that cause the most uncertain class predictions. This allows MUR to impose smoothness on a wider area in the input-output manifold. Our experiments show clear improvements in classification errors of various CR based methods when they are combined with VBI or MUR or both.

We present a new nonparametric mixture-of-experts model for multivariate regression problems, inspired by the probabilistic $k$-nearest neighbors algorithm. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point, yielding predictive distributions represented by Gaussian mixtures. Posterior inference is performed on the parameters of the mixture components as well as the distance metric using a mean-field variational Bayes algorithm accompanied with a stochastic gradient-based optimization procedure. The proposed method is especially advantageous in settings where inputs are of relatively high dimension in comparison to the data size, where input--output relationships are complex, and where predictive distributions may be skewed or multimodal. Computational studies on two synthetic datasets and one dataset comprising dose statistics of radiation therapy treatment plans show that our mixture-of-experts method outperforms a Gaussian process benchmark model both in terms of validation metrics and visual inspection.

Human judgments of word similarity have been a popular method of evaluating the quality of word embedding. But it fails to measure the geometry properties such as asymmetry. For example, it is more natural to say "Ellipses are like Circles" than "Circles are like Ellipses". Such asymmetry has been observed from a psychoanalysis test called word evocation experiment, where one word is used to recall another. Although useful, such experimental data have been significantly understudied for measuring embedding quality. In this paper, we use three well-known evocation datasets to gain insights into asymmetry encoding of embedding. We study both static embedding as well as contextual embedding, such as BERT. Evaluating asymmetry for BERT is generally hard due to the dynamic nature of embedding. Thus, we probe BERT's conditional probabilities (as a language model) using a large number of Wikipedia contexts to derive a theoretically justifiable Bayesian asymmetry score. The result shows that contextual embedding shows randomness than static embedding on similarity judgments while performing well on asymmetry judgment, which aligns with its strong performance on "extrinsic evaluations" such as text classification. The asymmetry judgment and the Bayesian approach provides a new perspective to evaluate contextual embedding on intrinsic evaluation, and its comparison to similarity evaluation concludes our work with a discussion on the current state and the future of representation learning.

With the growing number of published functional magnetic resonance imaging (fMRI) studies, meta-analysis databases and models have become an integral part of brain mapping research. Coordinate-based meta-analysis (CBMA) databases are built by automatically extracting both coordinates of reported peak activations and term associations using natural language processing (NLP) techniques. Solving term-based queries on these databases make it possible to obtain statistical maps of the brain related to specific cognitive processes. However, with tools like Neurosynth, only singleterm queries lead to statistically reliable results. When solving richer queries, too few studies from the database contribute to the statistical estimations. We design a probabilistic domain-specific language (DSL) standing on Datalog and one of its probabilistic extensions, CP-Logic, for expressing and solving rich logic-based queries. We encode a CBMA database into a probabilistic program. Using the joint distribution of its Bayesian network translation, we show that solutions of queries on this program compute the right probability distributions of voxel activations. We explain how recent lifted query processing algorithms make it possible to scale to the size of large neuroimaging data, where state of the art knowledge compilation (KC) techniques fail to solve queries fast enough for practical applications. Finally, we introduce a method for relating studies to terms probabilistically, leading to better solutions for conjunctive queries on smaller databases. We demonstrate results for two-term conjunctive queries, both on simulated meta-analysis databases and on the widely-used Neurosynth database.

DNA samples crime cases analysed in forensic genetics, frequently contain DNA from multiple contributors. These occur as convolutions of the DNA profiles of the individual contributors to the DNA sample. Thus, in cases where one or more of the contributors were unknown, an objective of interest would be the separation, often called deconvolution, of these unknown profiles. In order to obtain deconvolutions of the unknown DNA profiles, we introduced a multiple population evolutionary algorithm (MEA). We allowed the mutation operator of the MEA to utilise that the fitness is based on a probabilistic model and guide it by using the deviations between the observed and the expected value for every element of the encoded individual. This guided mutation operator (GM) was designed such that the larger the deviation the higher probability of mutation. Furthermore, the GM was inhomogeneous in time, decreasing to a specified lower bound as the number of iterations increased. We analysed 102 two-person DNA mixture samples in varying mixture proportions. The samples were quantified using two different DNA prep. kits: (1) Illumina ForenSeq Panel B (30 samples), and (2) Applied Biosystems Precision ID Globalfiler NGS STR panel (72 samples). The DNA mixtures were deconvoluted by the MEA and compared to the true DNA profiles of the sample. We analysed three scenarios where we assumed: (1) the DNA profile of the major contributor was unknown, (2) DNA profile of the minor was unknown, and (3) both DNA profiles were unknown. Furthermore, we conducted a series of sensitivity experiments on the ForenSeq panel by varying the sub-population size, comparing a completely random homogeneous mutation operator to the guided operator with varying mutation decay rates, and allowing for hill-climbing of the parent population.

Variational Bayesian phylogenetic inference (VBPI) provides a promising general variational framework for efficient estimation of phylogenetic posteriors. However, the current diagonal Lognormal branch length approximation would significantly restrict the quality of the approximating distributions. In this paper, we propose a new type of VBPI, VBPI-NF, as a first step to empower phylogenetic posterior estimation with deep learning techniques. By handling the non-Euclidean branch length space of phylogenetic models with carefully designed permutation equivariant transformations, VBPI-NF uses normalizing flows to provide a rich family of flexible branch length distributions that generalize across different tree topologies. We show that VBPI-NF significantly improves upon the vanilla VBPI on a benchmark of challenging real data Bayesian phylogenetic inference problems. Further investigation also reveals that the structured parameterization in those permutation equivariant transformations can provide additional amortization benefit.

Equation discovery, also known as symbolic regression, is a type of automated modeling that discovers scientific laws, expressed in the form of equations, from observed data and expert knowledge. Deterministic grammars, such as context-free grammars, have been used to limit the search spaces in equation discovery by providing hard constraints that specify which equations to consider and which not. In this paper, we propose the use of probabilistic context-free grammars in the context of equation discovery. Such grammars encode soft constraints on the space of equations, specifying a prior probability distribution on the space of possible equations. We show that probabilistic grammars can be used to elegantly and flexibly formulate the parsimony principle, that favors simpler equations, through probabilities attached to the rules in the grammars. We demonstrate that the use of probabilistic, rather than deterministic grammars, in the context of a Monte-Carlo algorithm for grammar-based equation discovery, leads to more efficient equation discovery. Finally, by specifying prior probability distributions over equation spaces, the foundations are laid for Bayesian approaches to equation discovery.