Some challenging problems in tracking multiple objects include the time-dependent cardinality, unordered measurements and object parameter labeling. In this paper, we employ Bayesian Bayesian nonparametric methods to address these challenges. In particular, we propose modeling the multiple object parameter state prior using the dependent Dirichlet and Pitman-Yor processes. These nonparametric models have been shown to be more flexible and robust, when compared to existing methods, for estimating the time-varying number of objects, providing object labeling and identifying measurement to object associations. Monte Carlo sampling methods are then proposed to efficiently learn the trajectory of objects from noisy measurements. Using simulations, we demonstrate the estimation performance advantage of the new methods when compared to existing algorithms such as the generalized labeled multi-Bernoulli filter.

Kernel methods augmented with random features give scalable algorithms for learning from big data. But it has been computationally hard to sample random features according to a probability distribution that is optimized for the data, so as to minimize the required number of features for achieving the learning to a desired accuracy. Here, we develop a quantum algorithm for sampling from this optimized distribution over features, in runtime $O(D)$ that is linear in the dimension $D$ of the input data. Our algorithm achieves an exponential speedup in $D$ compared to any known classical algorithm for this sampling task. In contrast to existing quantum machine learning algorithms, our algorithm circumvents sparsity and low-rank assumptions and thus has wide applicability. We also show that the sampled features can be combined with regression by stochastic gradient descent to achieve the learning without canceling out our exponential speedup. Our algorithm based on sampling optimized random features leads to an accelerated framework for machine learning that takes advantage of quantum computers.

When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is diagonalized and the original formulation. Although such a mapping requires a particular type of equality constraints, it is generalizable to some real problems such as efficient frontier for portfolio allocation and classification of Least Square Support Vector Machines (LSSVM). The established mapping could be potentially useful to explore optimal solutions in subspace, but it is not very clear to the author. This work was inspired by similar work proved on unconstrained formulation discussed earlier in \cite{Tan}, but its current proof is much improved and generalized. To the author's knowledge, very few similar discussion appears in literature.

This thesis contributes to the mathematical foundation of domain adaptation as emerging field in machine learning. In contrast to classical statistical learning, the framework of domain adaptation takes into account deviations between probability distributions in the training and application setting. Domain adaptation applies for a wider range of applications as future samples often follow a distribution that differs from the ones of the training samples. A decisive point is the generality of the assumptions about the similarity of the distributions. Therefore, in this thesis we study domain adaptation problems under as weak similarity assumptions as can be modelled by finitely many moments.

Statistical network analysis primarily focuses on inferring the parameters of an observed network. In many applications, especially in the social sciences, the observed data is the groups formed by individual subjects. In these applications, the network is itself a parameter of a statistical model. Zhao and Weko (2019) propose a model-based approach, called the hub model, to infer implicit networks from grouping behavior. The hub model assumes that each member of the group is brought together by a member of the group called the hub. The hub model belongs to the family of Bernoulli mixture models. Identifiability of parameters is a notoriously difficult problem for Bernoulli mixture models. This paper proves identifiability of the hub model parameters and estimation consistency under mild conditions. Furthermore, this paper generalizes the hub model by introducing a model component that allows hubless groups in which individual nodes spontaneously appear independent of any other individual. We refer to this additional component as the null component. The new model bridges the gap between the hub model and the degenerate case of the mixture model -- the Bernoulli product. Identifiability and consistency are also proved for the new model. Numerical studies are provided to demonstrate the theoretical results.

Stochastic block models (SBMs) are often used to find assortative community structures in networks, such that the probability of connections within communities is higher than in between communities. However, classic SBMs are not limited to assortative structures. In this study, we discuss the implications of this model-inherent indifference towards assortativity or disassortativity, and show that this characteristic can lead to undesirable outcomes for networks which are presupposedy assortative but which contain a reduced amount of information. To circumvent this issue, we introduce a constrained SBM that imposes strong assortativity constraints, along with efficient algorithmic approaches to solve it. These constraints significantly boost community recovery capabilities in regimes that are close to the information-theoretic threshold. They also permit to identify structurally-different communities in networks representing cerebral-cortex activity regions.

Did you enjoy reading or think it can be improved? Don't forget to leave your thoughts in the comments section below! If you liked this article, please share it with your friends, and read a few more!

In this paper, we deal with the problem of automatic tag recommendation for painting artworks. Diachronic descriptions containing deviations on the vocabulary used to describe each painting usually occur when the work is done by many experts over time. The objective of this work is to provide a framework that produces a more accurate and homogeneous set of tags for each painting in a large collection. To validate our method we build a model based on a weakly-supervised neural network for over $5{,}300$ paintings with hand-labeled descriptions made by experts for the paintings of the Brazilian painter Candido Portinari. This work takes place with the Portinari Project which started in 1979 intending to recover and catalog the paintings of the Brazilian painter. The Portinari paintings at that time were in private collections and museums spread around the world and thus inaccessible to the public. The descriptions of each painting were made by a large number of collaborators over 40 years as the paintings were recovered and these diachronic descriptions caused deviations on the vocabulary used to describe each painting. Our proposed framework consists of (i) a neural network that receives as input the image of each painting and uses frequent itemsets as possible tags, and (ii) a clustering step in which we group related tags based on the output of the pre-trained classifiers.

Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.

Causal inference methods are widely applied in the fields of medicine, policy, and economics. Central to these applications is the estimation of treatment effects to make decisions. Current methods make binary yes-or-no decisions based on the treatment effect of a single outcome dimension. These methods are unable to capture continuous space treatment policies with a measure of intensity. They also lack the capacity to consider the complexity of treatment such as matching candidate treatments with the subject. We propose to formulate the effectiveness of treatment as a parametrizable model, expanding to a multitude of treatment intensities and complexities through the continuous policy treatment function, and the likelihood of matching. Our proposal to decompose treatment effect functions into effectiveness factors presents a framework to model a rich space of actions using causal inference. We utilize deep learning to optimize the desired holistic metric space instead of predicting single-dimensional treatment counterfactual. This approach employs a population-wide effectiveness measure and significantly improves the overall effectiveness of the model. The performance of our algorithms is. demonstrated with experiments. When using generic continuous space treatments and matching architecture, we observe a 41% improvement upon prior art with cost-effectiveness and 68% improvement upon a similar method in the average treatment effect. The algorithms capture subtle variations in treatment space, structures the efficient optimizations techniques, and opens up the arena for many applications.