Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By analyzing these logs, we can learn process models that describe system procedures, predict the development of the system, or check whether the changes are expected. In this paper, we consider a novel technique that models these sequences of events in temporal-probabilistic manners. Specifically, we propose a probabilistic process model that combines hidden semi-Markov model and classification trees learning. Our experimental result shows that the proposed approach can answer a kind of question-"what are the most frequent sequence of system dynamics relevant to a given sequence of observable events?". For example, "Given a series of medical treatments, what are the most relevant patients' health condition pattern changes at different times?"

How can we build a learner that can capture the essence of what makes a hard problem more complex than a simple one, break the hard problem along characteristic lines into smaller problems it knows how to solve, and sequentially solve the smaller problems until the larger one is solved? To work towards this goal, we focus on learning to generalize in a particular family of problems that exhibit compositional and recursive structure: their solutions can be found by composing in sequence a set of reusable partial solutions. Our key idea is to recast the problem of generalization as a problem of learning algorithmic procedures: we can formulate a solution to this family as a sequential decision-making process over transformations between representations. Our formulation enables the learner to learn the structure and parameters of its own computation graph with sparse supervision, make analogies between problems by transforming one problem representation to another, and exploit modularity and reuse to scale to problems of varying complexity. Experiments on solving a variety of multilingual arithmetic problems demonstrate that our method discovers the hierarchical decomposition of a problem into its subproblems, generalizes out of distribution to unseen problem classes, and extrapolates to harder versions of the same problem, yielding a 10-fold reduction in sample complexity compared to a monolithic recurrent neural network.

Games generalize the optimization paradigm by introducing different objective functions for different optimizing agents, known as players. Generative Adversarial Networks (GANs) are arguably the most popular game formulation in recent machine learning literature. GANs achieve great results on generating realistic natural images, however they are known for being difficult to train. Training them involves finding a Nash equilibrium, typically performed using gradient descent on the two players' objectives. Game dynamics can induce rotations that slow down convergence to a Nash equilibrium, or prevent it altogether. We provide a theoretical analysis of the game dynamics. Our analysis, supported by experiments, shows that gradient descent with a negative momentum term can improve the convergence properties of some GANs.

We study the statistical properties of an estimator derived by applying a gradient ascent method with multiple initializations to a multi-modal likelihood function. We derive the population quantity that is the target of this estimator and study the properties of confidence intervals (CIs) constructed from asymptotic normality and the bootstrap approach. In particular, we analyze the coverage deficiency due to finite number of random initializations. We also investigate the CIs by inverting the likelihood ratio test, the score test, and the Wald test, and we show that the resulting CIs may be very different. We provide a summary of the uncertainties that we need to consider while making inference about the population. Note that we do not provide a solution to the problem of multiple local maxima; instead, our goal is to investigate the effect from local maxima on the behavior of our estimator. In addition, we analyze the performance of the EM algorithm under random initializations and derive the coverage of a CI with a finite number of initializations. Finally, we extend our analysis to a nonparametric mode hunting problem.

We study the problem of estimating heterogeneous treatment effects from observational data, where the treatment policy on the collected data was determined by potentially many confounding observable variables. We propose orthogonal random forest, an algorithm that combines orthogonalization, a technique that effectively removes the confounding effect in two-stage estimation, with generalized random forests [Athey et al., 2017], a flexible method for estimating treatment effect heterogeneity. We prove a consistency rate result of our estimator in the partially linear regression model, and en route we provide a consistency analysis for a general framework of performing generalized method of moments (GMM) estimation. We also provide a comprehensive empirical evaluation of our algorithms, and show that they consistently outperform baseline approaches.

We study a general online linear optimization problem(OLO). At each round, a subset of objects from a fixed universe of $n$ objects is chosen, and a linear cost associated with the chosen subset is incurred. We use \textit{regret} as a measure of performance of our algorithms. Regret is the difference between the total cost incurred over all iterations and the cost of the best fixed subset in hindsight. We consider \textit{Full Information}, \textit{Semi-Bandit} and \textit{Bandit} feedback for this problem. Using characteristic vectors of the subsets, this problem reduces to OLO on the $\{0,1\}^n$ hypercube. The Exp2 algorithm and its bandit variants are commonly used strategies for this problem. It was previously unknown if it is possible to run Exp2 on the hypercube in polynomial time. In this paper, we present a polynomial time algorithm called \textit{PolyExp} for OLO on the hypercube. We show that our algorithm is equivalent to both Exp2 on $\{0,1\}^n$ as well as Online Mirror Descent(OMD) with Entropic regularization on $[0,1]^n$ and Bernoulli Sampling. Under $L_\infty$ adversarial losses, in the Full Information case and Semi-Bandit case, analyzing Exp2 directly, gives an expected regret bound of $O(n^{3/2}\sqrt{T})$, whereas PolyExp yields a regret of $O(n\sqrt{T})$. In the Bandit case, analyzing Exp2 directly, gives an expected regret bound of $O(n^{2}\sqrt{T})$, whereas PolyExp yields a regret of $O(n^{3/2}\sqrt{T})$. This implies an improvement on Exp2's regret bound for these settings because of the equivalence. Moreover, PolyExp is minimax optimal in all the three settings as its regret bounds match the $L_\infty$ lowerbounds in \cite{audibert2011minimax}. Finally, we show how to use PolyExp on the $\{-1,+1\}^n$ hypercube, solving an open problem in \cite{bubeck2012towards}.

Given a convolutional dictionary underlying a set of observed signals, can a carefully designed auto-encoder recover the dictionary in the presence of noise? We introduce an auto-encoder architecture, termed constrained recurrent sparse auto-encoder (CRsAE), that answers this question in the affirmative. Given an input signal and an approximate dictionary, the encoder finds a sparse approximation using FISTA. The decoder reconstructs the signal by applying the dictionary to the output of the encoder. The encoder and decoder in CRsAE parallel the sparse-coding and dictionary update steps in optimization-based alternating-minimization schemes for dictionary learning. As such, the parameters of the encoder and decoder are not independent, a constraint which we enforce for the first time. We derive the back-propagation algorithm for CRsAE. CRsAE is a framework for blind source separation that, only knowing the number of sources (dictionary elements), and assuming sparsely-many can overlap, is able to separate them. We demonstrate its utility in the context of spike sorting, a source separation problem in computational neuroscience. We demonstrate the ability of CRsAE to recover the underlying dictionary and characterize its sensitivity as a function of SNR.

In sensor networks, it is not always practical to set up a fusion center. Therefore, there is need for fully decentralized clustering algorithms. Decentralized clustering algorithms should minimize the amount of data exchanged between sensors in order to reduce sensor energy consumption. In this respect, we propose one centralized and one decentralized clustering algorithm that work on compressed data without prior knowledge of the number of clusters. In the standard K-means clustering algorithm, the number of clusters is estimated by repeating the algorithm several times, which dramatically increases the amount of exchanged data, while our algorithm can estimate this number in one run. The proposed clustering algorithms derive from a theoretical framework establishing that, under asymptotic conditions, the cluster centroids are the only fixed-point of a cost function we introduce. This cost function depends on a weight function which we choose as the p-value of a Wald hypothesis test. This p-value measures the plausibility that a given measurement vector belongs to a given cluster. Experimental results show that our two algorithms are competitive in terms of clustering performance with respect to K-means and DB-Scan, while lowering by a factor at least $2$ the amount of data exchanged between sensors.

Modeling how individuals evolve over time is a fundamental problem in the natural and social sciences. However, existing datasets are often cross-sectional with each individual only observed at a single timepoint, making inference of temporal dynamics hard. Motivated by the study of human aging, we present a model that can learn temporal dynamics from cross-sectional data. Our model represents each individual with a low-dimensional latent state that consists of 1) a dynamic vector $rt$ that evolves linearly with time $t$, where $r$ is an individual-specific "rate of aging" vector, and 2) a static vector $b$ that captures time-independent variation. Observed features are a non-linear function of $rt$ and $b$. We prove that constraining the mapping between $rt$ and a subset of the observed features to be order-isomorphic yields a model class that is identifiable if the distribution of time-independent variation is known. Our model correctly recovers the latent rate vector $r$ in realistic synthetic data. Applied to the UK Biobank human health dataset, our model accurately reconstructs the observed data while learning interpretable rates of aging $r$ that are positively associated with diseases, mortality, and aging risk factors.

Imagine a state-of-the-art driverless car zipping along a road with a disabled, 90-year-old passenger. The car must make a decision: drive into the mother and child and kill them, or swerve into a wall and kill the passenger. This is a variation of the trolley problem, a thought experiment which dominates academic and popular thinking about the ethics of driverless cars. The problem is that such debates not only dismiss the complexity of the system in which driverless cars will exist, but are also moral red herrings. The real ethical issues lie in the politics and power concerns with driverless cars.