The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter estimation and model evaluation. However, the log-likelihood of complex models in fields such as computational biology and neuroscience is often intractable to compute analytically or numerically. In those cases, researchers can often only estimate the log-likelihood by comparing observed data with synthetic observations generated by model simulations. Standard techniques to approximate the likelihood via simulation either use summary statistics of the data or are at risk of producing severe biases in the estimate. Here, we explore another method, inverse binomial sampling (IBS), which can estimate the log-likelihood of an entire data set efficiently and without bias. For each observation, IBS draws samples from the simulator model until one matches the observation. The log-likelihood estimate is then a function of the number of samples drawn. The variance of this estimator is uniformly bounded, achieves the minimum variance for an unbiased estimator, and we can compute calibrated estimates of the variance. We provide theoretical arguments in favor of IBS and an empirical assessment of the method for maximum-likelihood estimation with simulation-based models. As case studies, we take three model-fitting problems of increasing complexity from computational and cognitive neuroscience. In all problems, IBS generally produces lower error in the estimated parameters and maximum log-likelihood values than alternative sampling methods with the same average number of samples. Our results demonstrate the potential of IBS as a practical, robust, and easy to implement method for log-likelihood evaluation when exact techniques are not available.

We consider the problem of learning a neural network classifier. Under the information bottleneck (IB) principle, we associate with this classification problem a representation learning problem, which we call "IB learning". We show that IB learning is, in fact, equivalent to a special class of the quantization problem. The classical results in rate-distortion theory then suggest that IB learning can benefit from a "vector quantization" approach, namely, simultaneously learning the representations of multiple input objects. Such an approach assisted with some variational techniques, result in a novel learning framework, "Aggregated Learning", for classification with neural network models. In this framework, several objects are jointly classified by a single neural network. The effectiveness of this framework is verified through extensive experiments on standard image recognition and text classification tasks. Introduction The revival of neural networks in the paradigm of deep learning (LeCun, Bengio, and Hinton 2015) has stimulated intense interest in understanding the networking of deep neural networks, e.g., (Shwartz-Ziv and Tishby 2017; Zhang et al. 2017). Among various efforts, an information-theoretic approach, information bottleneck (IB) (Tishby, Pereira, and Bialek 1999) stands out as a fundamental tool to theorize the learning of deep neural networks (Shwartz-Ziv and Tishby 2017; Saxe et al. 2018; Dai et al. 2018). Under the IB principle, the core of learning a neural network classifier is to find a representation T of the input example X, that contains as much as possible the information about X and as little as possible the information about the label Y .

Semi-supervised learning is a classification method which makes use of both labeled data and unlabeled data for training. In this paper, we propose a semi-supervised learning algorithm using a Bayesian semi-supervised model. We make a general assumption that the observations will follow two multivariate normal distributions depending on their true labels after the same unknown transformation. We use B-splines to put a prior on the transformation function for each component. To use unlabeled data in a semi-supervised setting, we assume the labels are missing at random. The posterior distributions can then be described using our assumptions, which we compute by the Gibbs sampling technique. The proposed method is then compared with several other available methods through an extensive simulation study. Finally we apply the proposed method in real data contexts for diagnosing breast cancer and classify radar returns. We conclude that the proposed method has better prediction accuracy in a wide variety of cases.

Autonomous systems are often required to operate in partially observable environments. They must reliably execute a specified objective even with incomplete information about the state of the environment. We propose a methodology to synthesize policies that satisfy a linear temporal logic formula in a partially observable Markov decision process (POMDP). By formulating a planning problem, we show how to use point-based value iteration methods to efficiently approximate the maximum probability of satisfying a desired logical formula and compute the associated belief state policy. We demonstrate that our method scales to large POMDP domains and provides strong bounds on the performance of the resulting policy.

To deal with the complexity of the new bigger and more complex generation of data, machine learning (ML) techniques are probably the first and foremost used. For ML algorithms to produce results in a reasonable amount of time, they need to be implemented efficiently. In this paper, we analyze one of the means to increase the performances of machine learning algorithms which is exploiting data locality. Data locality and access patterns are often at the heart of performance issues in computing systems due to the use of certain hardware techniques to improve performance. Altering the access patterns to increase locality can dramatically increase performance of a given algorithm. Besides, repeated data access can be seen as redundancy in data movement. Similarly, there can also be redundancy in the repetition of calculations. This work also identifies some of the opportunities for avoiding these redundancies by directly reusing computation results. We start by motivating why and how a more efficient implementation can be achieved by exploiting reuse in the memory hierarchy of modern instruction set processors. Next we document the possibilities of such reuse in some selected machine learning algorithms. Keywords: Increasing data locality, data redundancy and reuse, machine learning, supervised learners... Notice This an extended version of the paper titled "Reviewing Data Access Patterns and Computational Redundancy for Machine Learning Algorithms" that appeared in the proceedings of the IADIS International Conference Big Data Analytics, Data Mining and Computational Intelligence 2019 (part of MCCSIS 2019)" [19] The final publication of this article is available at IOS Press through http://dx.doi.org/10.3233/IDA-184287. Because processor speed is increasing at a much faster rate than memory speed, computer architects have turned increasingly to the use of memory hierarchies with one or more levels of cache memory. This caching technique takes advantage of data locality in programs which is the property that references to the same memory location (temporal locality) or adjacent locations (spatial locality) reused within a short period of time. 1 One of the most popular ways to increase it is to rewrite the data intensive parts of the program, almost always the loops [14]. A simple example of this is to interchange the two loops in Algorithm 1 such that the code looks like Algorithm 2; note that the indices in the loop headers have changed.

We consider the problem of discriminatively learning restricted Boltzmann machines in the presence of relational data. Unlike previous approaches that employ a rule learner (for structure learning) and a weight learner (for parameter learning) sequentially, we develop a gradient-boosted approach that performs both simultaneously. Our approach learns a set of weak relational regression trees, whose paths from root to leaf are conjunctive clauses and represent the structure, and whose leaf values represent the parameters. When the learned relational regression trees are transformed into a lifted RBM, its hidden nodes are precisely the conjunctive clauses derived from the relational regression trees. This leads to a more interpretable and explainable model. Our empirical evaluations clearly demonstrate this aspect, while displaying no loss in effectiveness of the learned models.

We present several new results on the feasibility of inferring the hidden states in strongly-connected trackable weak models. Here, a weak model is a directed graph in which each node is assigned a set of colors which may be emitted when that node is visited. A hypothesis is a node sequence which is consistent with a given color sequence. A weak model is said to be trackable if the worst case number of such hypotheses grows as a polynomial in the sequence length. We show that the number of hypotheses in strongly-connected trackable models is bounded by a constant and give an expression for this constant. We also consider the problem of reconstructing which branch was taken at a node with same-colored out-neighbors, and show that it is always eventually possible to identify which branch was taken if the model is strongly connected and trackable. We illustrate these properties by assigning transition probabilities and employing standard tools for analyzing Markov chains. In addition, we present new results for the entropy rates of weak models according to whether they are trackable or not. These theorems indicate that the combination of trackability and strong connectivity dramatically simplifies the task of reconstructing which nodes were visited. This work has implications for any problem which can be described in terms of an agent traversing a colored graph, such as the reconstruction of hidden states in a hidden Markov model (HMM).

To ensure the security of the general mass, crime prevention is one of the most higher priorities for any government. An accurate crime prediction model can help the government, law enforcement to prevent violence, detect the criminals in advance, allocate the government resources, and recognize problems causing crimes. To construct any future-oriented tools, examine and understand the crime patterns in the earliest possible time is essential. In this paper, I analyzed a real-world crime and accident dataset of Denver county, USA, from January 2014 to May 2019, which containing 478,578 incidents. This project aims to predict and highlights the trends of occurrence that will, in return, support the law enforcement agencies and government to discover the preventive measures from the prediction rates. At first, I apply several statistical analysis supported by several data visualization approaches. Then, I implement various classification algorithms such as Random Forest, Decision Tree, AdaBoost Classifier, Extra Tree Classifier, Linear Discriminant Analysis, K-Neighbors Classifiers, and 4 Ensemble Models to classify 15 different classes of crimes. The outcomes are captured using two popular test methods: train-test split, and k-fold cross-validation. Moreover, to evaluate the performance flawlessly, I also utilize precision, recall, F1-score, Mean Squared Error (MSE), ROC curve, and paired-T-test. Except for the AdaBoost classifier, most of the algorithms exhibit satisfactory accuracy. Random Forest, Decision Tree, Ensemble Model 1, 3, and 4 even produce me more than 90% accuracy. Among all the approaches, Ensemble Model 4 presented superior results for every evaluation basis. This study could be useful to raise the awareness of peoples regarding the occurrence locations and to assist security agencies to predict future outbreaks of violence in a specific area within a particular time.

Approximate linear programs (ALPs) are well-known models based on value function approximations (VFAs) to obtain heuristic policies and lower bounds on the optimal policy cost of Markov decision processes (MDPs). The ALP VFA is a linear combination of predefined basis functions that are chosen using domain knowledge and updated heuristically if the ALP optimality gap is large. We side-step the need for such basis function engineering in ALP -- an implementation bottleneck -- by proposing a sequence of ALPs that embed increasing numbers of random basis functions obtained via inexpensive sampling. We provide a sampling guarantee and show that the VFAs from this sequence of models converge to the exact value function. Nevertheless, the performance of the ALP policy can fluctuate significantly as more basis functions are sampled. To mitigate these fluctuations, we "self-guide" our convergent sequence of ALPs using past VFA information such that a worst-case measure of policy performance is improved. We perform numerical experiments on perishable inventory control and generalized joint replenishment applications, which, respectively, give rise to challenging discounted-cost MDPs and average-cost semi-MDPs. We find that self-guided ALPs (i) significantly reduce policy cost fluctuations and improve the optimality gaps from an ALP approach that employs basis functions tailored to the former application, and (ii) deliver optimality gaps that are comparable to a known adaptive basis function generation approach targeting the latter application. More broadly, our methodology provides application-agnostic policies and lower bounds to benchmark approaches that exploit application structure.

A variety of lifted inference algorithms, which exploit model symmetry to reduce computational cost, have been proposed to render inference tractable in probabilistic relational models. Most existing lifted inference algorithms operate only over discrete domains or continuous domains with restricted potential functions, e.g., Gaussian. We investigate two approximate lifted variational approaches that are applicable to hybrid domains and expressive enough to capture multi-modality. We demonstrate that the proposed variational methods are both scalable and can take advantage of approximate model symmetries, even in the presence of a large amount of continuous evidence. We demonstrate that our approach compares favorably against existing message-passing based approaches in a variety of settings. Finally, we present a sufficient condition for the Bethe approximation to yield a non-trivial estimate over the marginal polytope.