Machine learning has made major advances in categorizing objects in images, yet the best algorithms miss important aspects of how people learn and think about categories. People can learn richer concepts from fewer examples, including causal models that explain how members of a category are formed. Here, we explore the limits of this human ability to infer causal "programs" -- latent generating processes with nontrivial algorithmic properties -- from one, two, or three visual examples. People were asked to extrapolate the programs in several ways, for both classifying and generating new examples. As a theory of these inductive abilities, we present a Bayesian program learning model that searches the space of programs for the best explanation of the observations. Although variable, people's judgments are broadly consistent with the model and inconsistent with several alternatives, including a pre-trained deep neural network for object recognition, indicating that people can learn and reason with rich algorithmic abstractions from sparse input data.

The Cox proportional hazards model is ubiquitous in the analysis of time-to-event data. However, when the data dimension p is comparable to the sample size $N$, maximum likelihood estimates for its regression parameters are known to be biased or break down entirely due to overfitting. This prompted the introduction of the so-called regularized Cox model. In this paper we use the replica method from statistical physics to investigate the relationship between the true and inferred regression parameters in regularized multivariate Cox regression with L2 regularization, in the regime where both p and N are large but with p/N ~ O(1). We thereby generalize a recent study from maximum likelihood to maximum a posteriori inference. We also establish a relationship between the optimal regularization parameter and p/N, allowing for straightforward overfitting corrections in time-to-event analysis.

The standard Gibbs sampler of Mixed Multinomial Logit (MMNL) models involves sampling from conditional densities of utility parameters using Metropolis-Hastings (MH) algorithm due to unavailability of conjugate prior for logit kernel. To address this non-conjugacy concern, we propose the application of P\'olygamma data augmentation (PG-DA) technique for the MMNL estimation. The posterior estimates of the augmented and the default Gibbs sampler are similar for two-alternative scenario (binary choice), but we encounter empirical identification issues in the case of more alternatives ($J \geq 3$).

Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be specified in advance. In this article, a novel Bayesian model for simultaneous and automatic selection of the appropriate dimension of the latent space and the number of blocks is proposed. Extensions to directed and bipartite graphs are discussed. The model is tested on simulated and real world network data, showing promising performance for recovering latent community structure.

Given a set of empirical observations, conditional density estimation aims to capture the statistical relationship between a conditional variable $\mathbf{x}$ and a dependent variable $\mathbf{y}$ by modeling their conditional probability $p(\mathbf{y}|\mathbf{x})$. The paper develops best practices for conditional density estimation for finance applications with neural networks, grounded on mathematical insights and empirical evaluations. In particular, we introduce a noise regularization and data normalization scheme, alleviating problems with over-fitting, initialization and hyper-parameter sensitivity of such estimators. We compare our proposed methodology with popular semi- and non-parametric density estimators, underpin its effectiveness in various benchmarks on simulated and Euro Stoxx 50 data and show its superior performance. Our methodology allows to obtain high-quality estimators for statistical expectations of higher moments, quantiles and non-linear return transformations, with very little assumptions about the return dynamic.

In this paper, we consider advancing web-scale knowledge extraction and alignment by integrating OpenIE extractions in the form of (subject, predicate, object) triples with Knowledge Bases (KB). Traditional techniques from universal schema and from schema mapping fall in two extremes: either they perform instance-level inference relying on embedding for (subject, object) pairs, thus cannot handle pairs absent in any existing triples; or they perform predicate-level mapping and completely ignore background evidence from individual entities, thus cannot achieve satisfying quality. We propose OpenKI to handle sparsity of OpenIE extractions by performing instance-level inference: for each entity, we encode the rich information in its neighborhood in both KB and OpenIE extractions, and leverage this information in relation inference by exploring different methods of aggregation and attention. In order to handle unseen entities, our model is designed without creating entity-specific parameters. Extensive experiments show that this method not only significantly improves state-of-the-art for conventional OpenIE extractions like ReVerb, but also boosts the performance on OpenIE from semi-structured data, where new entity pairs are abundant and data are fairly sparse.

Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this research, we use deep generative models to develop two new semi-supervised Bayesian models for reject inference in credit scoring, in which we model the data generating process to be dependent on a Gaussian mixture. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. Our proposed models infer the unknown creditworthiness of the rejected applications by exact enumeration of the two possible outcomes of the loan (default or non-default). The efficient stochastic gradient optimization technique used in deep generative models makes our models suitable for large data sets. Finally, the experiments in this research show that our proposed models perform better than classical and alternative machine learning models for reject inference in credit scoring.

Nanowire field-effect sensors have recently been developed for label-free detection of biomolecules. In this work, we introduce a computational technique based on Bayesian estimation to determine the physical parameters of the sensor and, more importantly, the properties of the analyte molecules. To that end, we first propose a PDE based model to simulate the device charge transport and electrochemical behavior. Then, the adaptive Metropolis algorithm with delayed rejection (DRAM) is applied to estimate the posterior distribution of unknown parameters, namely molecule charge density, molecule density, doping concentration, and electron and hole mobilities. We determine the device and molecules properties simultaneously, and we also calculate the molecule density as the only parameter after having determined the device parameters. This approach makes it possible not only to determine unknown parameters, but it also shows how well each parameter can be determined by yielding the probability density function (pdf).

The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood estimate of intrinsic dimension for flat manifolds. The proposed algorithm (GeoMLE) realizes the correction by regression of standard MLEs based on distances to nearest neighbors for different sizes of neighborhoods. Moreover, the proposed approach also efficiently handles the case of nonuniform sampling of the manifold. We perform numerous experiments on different synthetic and real-world datasets. The results show that our algorithm achieves state-of-the-art performance, while also being computationally efficient and robust to noise in the data.

We propose a supervised anomaly detection method based on neural density estimators, where the negative log likelihood is used for the anomaly score. Density estimators have been widely used for unsupervised anomaly detection. By the recent advance of deep learning, the density estimation performance has been greatly improved. However, the neural density estimators cannot exploit anomaly label information, which would be valuable for improving the anomaly detection performance. The proposed method effectively utilizes the anomaly label information by training the neural density estimator so that the likelihood of normal instances is maximized and the likelihood of anomalous instances is lower than that of the normal instances. We employ an autoregressive model for the neural density estimator, which enables us to calculate the likelihood exactly. With the experiments using 16 datasets, we demonstrate that the proposed method improves the anomaly detection performance with a few labeled anomalous instances, and achieves better performance than existing unsupervised and supervised anomaly detection methods.