You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood). It just so happens that for an observation that we assume to be drawn from a Gaussian random variable, the likelihood function usually takes a nice form after you take a logarithm. Then there is usually a leading negation, encouraging the entrepreneurial optimizer to switch away from maximizing the objective to minimizing the negative of objective, or roughly the "cost". For discrete maximum likelihood estimation the "cost" also has another meaningful name since it takes the same form as the euclidean distance in the observation space.

We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization, and we focus on the special case of Bayesian optimization, using the rollout algorithm and some of its variations. We then discuss the more general case of sequential estimation of a random vector using optimal measurement selection, and its application to problems of stochastic and adaptive control. We distinguish between adaptive control of deterministic and stochastic systems: the former are better suited for the use of rollout, while the latter are well suited for the use of rollout with certainty equivalence approximations. As an example of the deterministic case, we discuss sequential decoding problems, and a rollout algorithm for the approximate solution of the Wordle and Mastermind puzzles, recently developed in the paper [BBB22].

Model estimates obtained from traditional subspace identification methods may be subject to significant variance. This elevated variance is aggravated in the cases of large models or of a limited sample size. Common solutions to reduce the effect of variance are regularized estimators, shrinkage estimators and Bayesian estimation. In the current work we investigate the latter two solutions, which have not yet been applied to subspace identification. Our experimental results show that our proposed estimators may reduce the estimation risk up to $40\%$ of that of traditional subspace methods.

Rapid advancements in collection, processing, and dissemination of multi-platform molecular and genomics (multi-omics, in short) data has resulted in enormous opportunities to aggregate such data in order to understand, prevent, and treat diseases. This has catalyzed development of integrative methods that can collectively mine multiple types and scales of multi-omics data, in order to provide a more holistic view of human disease evolution and progression (Subramanian et al. 2020). Specifically, in the context of cancer, a disease driven predominantly by agglomerations of several molecular changes (Sun et al. 2021), the importance of synthesizing information from multi-platform omics and clinical sources to understand the cellular basis of the disease is even further underscored. Cellular oncological mechanisms, triggered at different molecular levels of the DNA RNA Protein path, can confer profound phenotypic advantages/disadvantages. While significant improvements have been made in multi-omics data integration methods to unveil such mechanisms, focused on both prognosis (Duan et al. 2021) and treatment (Finotello et al. 2020), the precise functions governing them need detailed and data-driven de-novo evaluations. Our work, in the same vein, aims at two different but inter-related scientific axes: (i) selection of biomarkers associated with cancer prognosis and clinical outcomes, and (ii) learning the mechanism of these biomarkers' effects upon such outcomes via integrating upstream molecular information - we provide some additional scientific context below. Classes of Integrative Omics Models First, we briefly discuss existing integrative omics approaches in order to contextualize the need for our framework. Broadly, most of the existing integrative statistical methods can be classified into two categories - horizontal (meta-analysis type) and vertical (multi-omics) integration procedures (Tseng et al. 2015).

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal dependence, the inverse problem can be severely ill-posed with a data-dependent singular inversion operator. The Bayesian approach overcomes the ill-posedness through a non-degenerate prior. However, a fixed non-degenerate prior leads to a divergent posterior mean when the observation noise becomes small, if the data induces a perturbation in the eigenspace of zero eigenvalues of the inversion operator. We introduce a data-adaptive prior to achieve a stable posterior whose mean always has a small noise limit. The data-adaptive prior's covariance is the inversion operator with a hyper-parameter selected adaptive to data by the L-curve method. Furthermore, we provide a detailed analysis on the computational practice of the data-adaptive prior, and demonstrate it on Toeplitz matrices and integral operators. Numerical tests show that a fixed prior can lead to a divergent posterior mean in the presence of any of the four types of errors: discretization error, model error, partial observation and wrong noise assumption. In contrast, the data-adaptive prior always attains posterior means with small noise limits.

This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse topology) rather than fully specified. Such partial knowledge provides constraints on the input probability measures. The theory of Optimal Uncertainty Quantification allows us to convert the task into a constraint optimization problem where one seeks to compute the least upper/greatest lower bound of the system's output uncertainties by finding the extremal probability measure of the input. Such optimization requires repeated evaluation of the system's performance indicator (input to performance map) and is high-dimensional and non-convex by nature. Therefore, it is difficult to find the optimal uncertainty bounds in practice. In this paper, we examine the use of machine learning, especially deep neural networks, to address the challenge. We achieve this by introducing a neural network classifier to approximate the performance indicator combined with the stochastic gradient descent method to solve the optimization problem. We demonstrate the learning based framework on the uncertainty quantification of the impact of magnesium alloys, which are promising light-weight structural and protective materials. Finally, we show that the approach can be used to construct maps for the performance certificate and safety design in engineering practice.

Traditional network embedding primarily focuses on learning a continuous vector representation for each node, preserving network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily applied to the vector-format node representations for network analysis. However, the learned continuous vector representations are inefficient for large-scale similarity search, which often involves finding nearest neighbors measured by distance or similarity in a continuous vector space. In this paper, we propose a search efficient binary network embedding algorithm called BinaryNE to learn a binary code for each node, by simultaneously modeling node context relations and node attribute relations through a three-layer neural network. BinaryNE learns binary node representations through a stochastic gradient descent based online learning algorithm. The learned binary encoding not only reduces memory usage to represent each node, but also allows fast bit-wise comparisons to support faster node similarity search than using Euclidean distance or other distance measures. Extensive experiments and comparisons demonstrate that BinaryNE not only delivers more than 25 times faster search speed, but also provides comparable or better search quality than traditional continuous vector based network embedding methods. The binary codes learned by BinaryNE also render competitive performance on node classification and node clustering tasks. The source code of this paper is available at https://github.com/daokunzhang/BinaryNE.

G-Enum histograms are a new fast and fully automated method for irregular histogram construction. By framing histogram construction as a density estimation problem and its automation as a model selection task, these histograms leverage the Minimum Description Length principle (MDL) to derive two different model selection criteria. Several proven theoretical results about these criteria give insights about their asymptotic behavior and are used to speed up their optimisation. These insights, combined to a greedy search heuristic, are used to construct histograms in linearithmic time rather than the polynomial time incurred by previous works. The capabilities of the proposed MDL density estimation method are illustrated with reference to other fully automated methods in the literature, both on synthetic and large real-world data sets.

We study a new approach to learning energy-based models (EBMs) based on adversarial training (AT). We show that (binary) AT learns a special kind of energy function that models the support of the data distribution, and the learning process is closely related to MCMC-based maximum likelihood learning of EBMs. We further propose improved techniques for generative modeling with AT, and demonstrate that this new approach is capable of generating diverse and realistic images. Aside from having competitive image generation performance to explicit EBMs, the studied approach is stable to train, is well-suited for image translation tasks, and exhibits strong out-of-distribution adversarial robustness. Our results demonstrate the viability of the AT approach to generative modeling, suggesting that AT is a competitive alternative approach to learning EBMs.

Legal Judgment Prediction is one of the most acclaimed fields for the combined area of NLP, AI, and Law. By legal prediction we mean an intelligent systems capable to predict specific judicial characteristics, such as judicial outcome, a judicial class, predict an specific case. In this research, we have used AI classifiers to predict judicial outcomes in the Brazilian legal system. For this purpose, we developed a text crawler to extract data from the official Brazilian electronic legal systems. These texts formed a dataset of second-degree murder and active corruption cases. We applied different classifiers, such as Support Vector Machines and Neural Networks, to predict judicial outcomes by analyzing textual features from the dataset. Our research showed that Regression Trees, Gated Recurring Units and Hierarchical Attention Networks presented higher metrics for different subsets. As a final goal, we explored the weights of one of the algorithms, the Hierarchical Attention Networks, to find a sample of the most important words used to absolve or convict defendants.