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Least-mean-squares (LMS) solvers such as Linear / Ridge-Regression and SVD not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as matrix factorizations. We suggest an algorithm that gets a finite set of n d-dimensional real vectors and returns a subset of d+1 vectors with positive weights whose weighted sum is exactly the same. The constructive proof in Caratheodory's Theorem computes such a subset in O(n

We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a model trained on the coreset is provably competitive with that trained on the original data set. Since the size of the coreset is generally much smaller than the original set, our preprocess-then-train scheme has potential to lead to significant speedups when training SVM models. We prove lower and upper bounds on the size of the coreset required to obtain small data summaries for the SVM problem. As a corollary, we show that our algorithm can be used to extend the applicability of any off-the-shelf SVM solver to streaming, distributed, and dynamic data settings. We evaluate the performance of our algorithm on real-world and synthetic data sets. Our experimental results reaffirm the favorable theoretical properties of our algorithm and demonstrate its practical effectiveness in accelerating SVM training.

Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction is done in a problem dependent manner and it could take years to design and prove the correctness of a coreset for a specific family of queries. This could limit coresets use in practical applications. Moreover, small coresets provably do not exist for many problems. To address these limitations, we propose a generic, learning-based algorithm for construction of coresets. Our approach offers a new definition of coreset, which is a natural relaxation of the standard definition and aims at approximating the \emph{average} loss of the original data over the queries. This allows us to use a learning paradigm to compute a small coreset of a given set of inputs with respect to a given loss function using a training set of queries. We derive formal guarantees for the proposed approach. Experimental evaluation on deep networks and classic machine learning problems show that our learned coresets yield comparable or even better results than the existing algorithms with worst-case theoretical guarantees (that may be too pessimistic in practice). Furthermore, our approach applied to deep network pruning provides the first coreset for a full deep network, i.e., compresses all the network at once, and not layer by layer or similar divide-and-conquer methods.

Major societal and environmental challenges involve complex systems that have diverse multi-scale interacting processes. Consider, for example, how droughts and water reserves affect crop production and how agriculture and industrial needs affect water quality and availability. Preventive measures, such as delaying planting dates and adopting new agricultural practices in response to changing weather patterns, can reduce the damage caused by natural processes. Understanding how these natural and human processes affect one another allows forecasting the effects of undesirable situations and study interventions to take preventive measures. For many of these processes, there are expert models that incorporate state-of-the-art theories and knowledge to quantify a system's response to a diversity of conditions. A major challenge for efficient modeling is the diversity of modeling approaches across disciplines and the wide variety of data sources available only in formats that require complex conversions. Using expert models for particular problems requires integration of models with third-party data as well as integration of models across disciplines. Modelers face significant heterogeneity that requires resolving semantic, spatiotemporal, and execution mismatches, which are largely done by hand today and may take more than 2 years of effort. We are developing a modeling framework that uses artificial intelligence (AI) techniques to reduce modeling effort while ensuring utility for decision making. Our work to date makes several innovative contributions: (1) an intelligent user interface that guides analysts to frame their modeling problem and assists them by suggesting relevant choices and automating steps along the way; (2) semantic metadata for models, including their modeling variables and constraints, that ensures model relevance and proper use for a given decision-making problem; and (3) semantic representations of datasets in terms of modeling variables that enable automated data selection and data transformations. This framework is implemented in the MINT (Model INTegration) framework, and currently includes data and models to analyze the interactions between natural and human systems involving climate, water availability, agricultural production, and markets. Our work to date demonstrates the utility of AI techniques to accelerate modeling to support decision-making and uncovers several challenging directions for future work.

We develop and analyze a method to reduce the size of a very large set of data points in a high dimensional Euclidean space R d to a small set of weighted points such that the result of a predetermined data analysis task on the reduced set is approximately the same as that for the original point set. For example, computing the first k principal components of the reduced set will return approximately the first k principal components of the original set or computing the centers of a k-means clustering on the reduced set will return an approximation for the original set. Such a reduced set is also known as a coreset. The main new feature of our construction is that the cardinality of the reduced set is independent of the dimension d of the input space and that the sets are mergable. The latter property means that the union of two reduced sets is a reduced set for the union of the two original sets (this property has recently also been called composability, see Indyk et. al., PODS 2014). It allows us to turn our methods into streaming or distributed algorithms using standard approaches. For problems such as k-means and subspace approximation the coreset sizes are also independent of the number of input points. Our method is based on projecting the points on a low dimensional subspace and reducing the cardinality of the points inside this subspace using known methods. The proposed approach works for a wide range of data analysis techniques including k-means clustering, principal component analysis and subspace clustering. The main conceptual contribution is a new coreset definition that allows to charge costs that appear for every solution to an additive constant., The conference version of this work appeared at SODA 2013

A common technique for compressing a neural network is to compute the k-rank ℓ2 approximation Ak of the matrix A∈Rn×d via SVD that corresponds to a fully connected layer (or embedding layer). Here, d is the number of input neurons in the layer, n is the number in the next one, and Ak is stored in O((n+d)k) memory instead of O(nd). Then, a fine-tuning step is used to improve this initial compression. However, end users may not have the required computation resources, time, or budget to run this fine-tuning stage. Furthermore, the original training set may not be available. In this paper, we provide an algorithm for compressing neural networks using a similar initial compression time (to common techniques) but without the fine-tuning step. The main idea is replacing the k-rank ℓ2 approximation with ℓp, for p∈[1,2], which is known to be less sensitive to outliers but much harder to compute. Our main technical result is a practical and provable approximation algorithm to compute it for any p≥1, based on modern techniques in computational geometry. Extensive experimental results on the GLUE benchmark for compressing the networks BERT, DistilBERT, XLNet, and RoBERTa confirm this theoretical advantage.

Fadi Abu Baker,1 Amir Mari,1 Kamal Aamarney,2 Abu Ras Hakeem,3 Barouch Ovadia,1 Yael Kopelman,11Gastroenterology and Hepatology Department, Hillel Yaffe Medical Center, affiliated to the Ruth and Rappaport Faculty of Medicine, Haifa, Israel; 2Pharmacy Services Department, Hillel Yaffe Medical Center, affiliated to the Ruth and Rappaport Faculty of Medicine, Haifa, Israel; 3Anesthesiology Department, Hillel Yaffe Medical Center, affiliated to the Ruth and Rappaport Faculty of Medicine, Haifa, Israel Background: Propofol-mediated sedation is safe and clearly associated with increased patient satisfaction. However, whether it results in a favorable effect on colonoscopy outcomes and performance compared to standard sedation with benzodiazepines/opiates remains unclear.Objectives: To determine the effect of propofol-mediated sedation on colonoscopy-quality measures compared to traditional sedation.Methods: A large cohort of 44,794 patients who had undergone sedated colonoscopies were included. Colonoscopy-quality indicators were examined in benzodiazepine/opiate-sedated patients and compared with a propofol-mediated sedation group. Adjustment for potential confounders, such as age, sex, quality of bowel preparation, procedural setting, and indication was performed.Results: Patients who received propofol-mediated sedation were more likely, and in a dose-dependent manner, to have an enhanced polyp-detection rate (22.8% vs 20.9%, P

An $\varepsilon$-coreset for Least-Mean-Squares (LMS) of a matrix $A\in{\mathbb{R}}^{n\times d}$ is a small weighted subset of its rows that approximates the sum of squared distances from its rows to every affine $k$-dimensional subspace of ${\mathbb{R}}^d$, up to a factor of $1\pm\varepsilon$. Such coresets are useful for hyper-parameter tuning and solving many least-mean-squares problems such as low-rank approximation ($k$-SVD), $k$-PCA, Lassso/Ridge/Linear regression and many more. Coresets are also useful for handling streaming, dynamic and distributed big data in parallel. With high probability, non-uniform sampling based on upper bounds on what is known as importance or sensitivity of each row in $A$ yields a coreset. The size of the (sampled) coreset is then near-linear in the total sum of these sensitivity bounds. We provide algorithms that compute provably \emph{tight} bounds for the sensitivity of each input row. It is based on two ingredients: (i) iterative algorithm that computes the exact sensitivity of each point up to arbitrary small precision for (non-affine) $k$-subspaces, and (ii) a general reduction of independent interest from computing sensitivity for the family of affine $k$-subspaces in ${\mathbb{R}}^d$ to (non-affine) $(k+1)$- subspaces in ${\mathbb{R}}^{d+1}$. Experimental results on real-world datasets, including the English Wikipedia documents-term matrix, show that our bounds provide significantly smaller and data-dependent coresets also in practice. Full open source is also provided.

A coreset of a dataset is a small weighted set, such that querying the coreset provably yields a ( 1 + &epsilon, )-factor approximation to the original (full) dataset, for a given family of queries. This paper suggests accurate coresets ( &epsilon, = 0 ) that are subsets of the input for fundamental optimization problems. These coresets enabled us to implement a &ldquo, Guardian Angel&rdquo, system that computes pose-estimation in a rate &gt, 20 frames per second. It tracks a toy quadcopter which guides guests in a supermarket, hospital, mall, airport, and so on. We prove that any set of n matrices in R d &times, d whose sum is a matrix S of rank r, has a coreset whose sum has the same left and right singular vectors as S, and consists of O ( d r ) = O ( d 2 ) matrices, independent of n. This implies the first (exact, weighted subset) coreset of O ( d 2 ) points to problems such as linear regression, PCA/SVD, and Wahba&rsquo, s problem, with corresponding streaming, dynamic, and distributed versions. Our main tool is a novel usage of the Caratheodory Theorem for coresets, an algorithm that computes its set in time that is linear in its cardinality. Extensive experimental results on both synthetic and real data, companion video of our system, and open code are provided.

We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a models trained on the coreset are provably competitive with those trained on the original data set. Since the size of the coreset is generally much smaller than the original set, our preprocess-then-train scheme has potential to lead to significant speedups when training SVM models. We prove lower and upper bounds on the size of the coreset required to obtain small data summaries for the SVM problem. As a corollary, we show that our algorithm can be used to extend the applicability of any off-the-shelf SVM solver to streaming, distributed, and dynamic data settings. We evaluate the performance of our algorithm on real-world and synthetic data sets. Our experimental results reaffirm the favorable theoretical properties of our algorithm and demonstrate its practical effectiveness in accelerating SVM training.

Understanding the interactions between natural processes and human activities poses major challenges as it requires the integration of models and data across disparate disciplines. It typically takes many months and even years to create valid end-to-end simulations as different models need to be configured in consistent ways and generate data that is usable by other models. MINT is a novel framework for model integration that captures extensive knowledge about models and data and aims to automatically compose them together. MINT guides a user to pose a well-formed modeling question, select and configure appropriate models, find and prepare appropriate datasets, compose data and models into end-to-end workflows, run the simulations, and visualize the results. MINT currently includes hydrology, agriculture, and socioeconomic models.

The PageRank algorithm is used by search engines to rank websites in their search results. The algorithm outputs a probability distribution that a person randomly clicking on links will arrive at any particular page. Intuitively, a node in the center of the network should be visited with high probability even if it has few edges, and an isolated node that has many (local) neighbours will be visited with low probability. The idea of PageRank is to rank nodes according to a stable state and not according to the previous local measurement of inner/outer edges from a node that may be manipulated more easily than the corresponding entry in the stable state.

Background: Traditionally, intubation of pregnant women has been performed using a rapid sequence induction. This is due to the classical concept that women with more than 18 weeks of pregnancy (mid-second trimester) are always considered to have an increased risk of aspiration due to a number of factors, regardless of the fasting duration. Rapid sequence induction is associated with a higher rate of adverse events. Aims: Our study aimed to illuminate the hypothesis that there is no difference in gastric volume between term-pregnant women and non-pregnant or first-trimester pregnant women who were undergoing minor gynecological surgical procedures. Accordingly, we measured gastric volume and content before anesthesia in term-pregnant women undergoing elective cesarean section, and to compare it with non-pregnant or first-trimester pregnant women who were undergoing minor gynecological surgical procedures. Methods: In this single-center prospective study, the gastric volume and content were assessed by abdominal ultrasound (AUS) just prior to the scheduled procedure. AUS was performed in the sagittal or para-sagittal plain in the upright position and the stomach content was estimated according to the antral circumferential area. Group 1 consisted of 50 term-pregnant women scheduled for cesarean section. Group 2 consisted of 45 non-pregnant or first-trimester pregnant women who were scheduled for minor gynecologic procedure. Results: Despite significant longer fasting time prior to the interventional procedure in the non-pregnant or first-trimester women group, there was no significant difference in gastric volume between term-pregnant and first-trimester pregnant women (3.2 ± 0.97 cm2 vs 3.2 ± 0.79 cm2; P = .97). Gastric volume was small in the two groups. Conclusion: Fasting gastric volume before cesarean section in term-pregnant women is small and is not different than in non-pregnant or first-trimester women undergoing minor gynecologic procedures. Ultrasound estimation of gastric volume is a reliable and easy-to-perform technique which might help in decision-making regarding the airway management prior to induction of anesthesia in pregnant women.

The k-means problem is to compute a set of k centers (points) that minimizes the sum of squared distances to a given set of n points in a metric space. Arguably, the most common algorithm to solve it is k-means++ which is easy to implement and provides a provably small approximation error in time that is linear in n. We generalize k-means++ to support outliers in two sense (simultaneously): (i) nonmetric spaces, e.g., M-estimators, where the distance dist(p,x) between a point p and a center x is replaced by mindist(p,x),c for an appropriate constant c that may depend on the scale of the input. (ii) k-means clustering with m&ge, 1 outliers, i.e., where the m farthest points from any given k centers are excluded from the total sum of distances. This is by using a simple reduction to the (k+m)-means clustering (with no outliers).

A brain-computer interface (BCI) based on the motor imagery (MI) paradigm translates one's motor intention into a control signal by classifying the Electroencephalogram (EEG) signal of different tasks. However, most existing systems either (i) use a high-quality algorithm to train the data off-line and run only classification in real-time, since the off-line algorithm is too slow, or (ii) use low-quality heuristics that are sufficiently fast for real-time training but introduces relatively large classification error. In this work, we propose a novel processing pipeline that allows real-time and parallel learning of EEG signals using high-quality but possibly inefficient algorithms. This is done by forging a link between BCI and core-sets, a technique that originated in computational geometry for handling streaming data via data summarization. We suggest an algorithm that maintains the representation such coreset tailored to handle the EEG signal which enables: (i) real time and continuous computation of the Common Spatial Pattern (CSP) feature extraction method on a coreset representation of the signal (instead on the signal itself) , (ii) improvement of the CSP algorithm efficiency with provable guarantees by applying CSP algorithm on the coreset, and (iii) real time addition of the data trials (EEG data windows) to the coreset. For simplicity, we focus on the CSP algorithm, which is a classic algorithm. Nevertheless, we expect that our coreset will be extended to other algorithms in future papers. In the experimental results we show that our system can indeed learn EEG signals in real-time for example a 64 channels setup with hundreds of time samples per second. Full open source is provided to reproduce the experiment and in the hope that it will be used and extended to more coresets and BCI applications in the future.

Magnesium is an essential intracellular cation. Magnesium deficiency is common in the general population and its prevalence among patients with cirrhosis is even higher. Correlation between serum levels and total body content is poor because most magnesium is intracellular. Minimal hepatic encephalopathy is a subclinical phase of hepatic encephalopathy with no overt symptoms. Cognitive exams can reveal minor changes in coordination, attention, and visuomotor function, whereas language and verbal intelligence are usually relatively spared.To assess the correlation between intracellular and serum magnesium levels and minimal hepatic encephalopathy.Outpatients with a diagnosis of compensated liver cirrhosis were enrolled in this randomized, double-blinded study. Patients were recruited for the study from November 2013 to January 2014, and were randomly assigned to a control (placebo) or an interventional (treated with magnesium oxide) group. Serum and intracellular magnesium levels were measured at enrollment and at the end of the study. Cognitive function was assessed by a specialized occupational therapist.Forty-two patients met the inclusion criteria, 29 of whom were included in this study. Among these, 83% had abnormal cognitive exam results compatible with minimal hepatic encephalopathy. While only 10% had hypomagnesemia, 33.3% had low levels of intracellular magnesium. Initial intracellular and serum magnesium levels positively correlated with cognitive performance.Magnesium deficiency is common among patients with compensated liver cirrhosis. We found an association between magnesium deficiency and impairment in several cognitive function tests. This finding suggests involvement of magnesium in the pathophysiology of minimal hepatic encephalopathy.

Whether the source is autonomous car, robotic vacuum cleaner, or a quadcopter, signals from sensors tend to have some hidden patterns that repeat themselves. For example, typical GPS traces from a smartphone contain periodic trajectories such as &ldquo, home, work, home, work, ⋯&rdquo, Our goal in this study was to automatically reverse engineer such signals, identify their periodicity, and then use it to compress and de-noise these signals. To do so, we present a novel method of using algorithms from the field of pattern matching and text compression to represent the &ldquo, language&rdquo, in such signals. Common text compression algorithms are less tailored to handle such strings. Moreover, they are lossless, and cannot be used to recover noisy signals. To this end, we define the recursive run-length encoding (RRLE) method, which is a generalization of the well known run-length encoding (RLE) method. Then, we suggest lossy and lossless algorithms to compress and de-noise such signals. Unlike previous results, running time and optimality guarantees are proved for each algorithm. Experimental results on synthetic and real data sets are provided. We demonstrate our system by showing how it can be used to turn commercial micro air-vehicles into autonomous robots. This is by reverse engineering their unpublished communication protocols and using a laptop or on-board micro-computer to control them. Our open source code may be useful for both the community of millions of toy robots users, as well as for researchers that may extend it for further protocols.

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational geometry, combinatorics and convex optimization. As an example application, we provide the first constant-factor approximation algorithms whose running-time is polynomial in $n$ for the fundamental problem of \emph{Points-to-Lines alignment}: Given $n$ points $p_1,\cdots,p_n$ and $n$ lines $\ell_1,\cdots,\ell_n$ on the plane and $z>0$, compute the matching $\pi:[n]\to[n]$ and alignment (rotation matrix $R$ and a translation vector $t$) that minimize the sum of Euclidean distances $\sum_{i=1}^n \mathrm{dist}(Rp_i-t,\ell_{\pi(i)})^z$ between each point to its corresponding line. This problem is non-trivial even if $z=1$ and the matching $\pi$ is given. If $\pi$ is given, the running time of our algorithms is $O(n^3)$, and even near-linear in $n$ using core-sets that support: streaming, dynamic, and distributed parallel computations in poly-logarithmic update time. Generalizations for handling e.g. outliers or pseudo-distances such as $M$-estimators for the problem are also provided. Experimental results and open source code show that our provable algorithms improve existing heuristics also in practice. A companion demonstration video in the context of Augmented Reality shows how such algorithms may be used in real-time systems.

The k-nearest neighbors (kNN) classifier predicts a class of a query, q, by taking the majority class of its k neighbors in an existing (already classified) database, S. In secure kNN, q and S are owned by two different parties and q is classified without sharing data. In this work we present a classifier based on kNN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider κ nearest neighbors for κ ≈k with probability that increases as the statistical distance between Gaussian and the distribution of the distances from q to S decreases. We call our classifier k-ish Nearest Neighbors (k-ish NN). For the implementation we introduce double-blinded coin-toss where the bias and output of the toss are encrypted. We use it to approximate the average and variance of the distances from q to S in a scalable circuit whose depth is independent of |S|. We believe these to be of independent interest. We implemented our classifier in an open source library based on HElib and tested it on a breast tumor database. Our classifier has accuracy and running time comparable to current state of the art (non-HE) MPC solution that have better running time but worse communication complexity. It also has communication complexity similar to naive HE implementation that have worse running time.

Standard hedonic house pricing assumes that house prices are independent of the intangible to be priced. A methodology is proposed in which the supply as well as the demand for housing depends on the intangible. The methodology is applied to value access to the Trans-Israel Highway (TIH). Using spatial panel data (2002–2008) we show that TIH had two effects on the housing market. It increased house prices in locations with greater access to TIH, and it affected housing construction. Standard hedonic pricing would have underestimated the value of access because it ignores the effects of housing construction on the intangible to be priced. House prices began to increase three years before TIH was inaugurated, but housing construction did not anticipate the inauguration of TIH.

The aim of this article is to present an example of a novel cloud computing infrastructure for big data analytics in the Process Control Industry. Latest innovations in the field of Process Analyzer Techniques (PAT), big data and wireless technologies have created a new environment in which almost all stages of the industrial process can be recorded and utilized, not only for safety, but also for real time optimization. Based on analysis of historical sensor data, machine learning based optimization models can be developed and deployed in real time closed control loops. However, still the local implementation of those systems requires a huge investment in hardware and software, as a direct result of the big data nature of sensors data being recorded continuously. The current technological advancements in cloud computing for big data processing, open new opportunities for the industry, while acting as an enabler for a significant reduction in costs, making the technology available to plants of all sizes. The main contribution of this article stems from the presentation for a fist time ever of a pilot cloud based architecture for the application of a data driven modeling and optimal control configuration for the field of Process Control. As it will be presented, these developments have been carried in close relationship with the process industry and pave a way for a generalized application of the cloud based approaches, towards the future of Industry 4.0 Integrated Process Control based on Distributed In-Situ Sensors into Raw Material and Energy Feedstock, DISIRE

Mobile sensor networks are a great source of data. By collecting data with mobile sensor nodes from individuals in a user community, e.g. using their smartphones, we can learn global information such as traffic congestion patterns in the city, location of key community facilities, and locations of gathering places. Can we publish and run queries on mobile sensor network databases without disclosing information about individual nodes? Differential privacy is a strong notion of privacy which guarantees that very little will be learned about individual records in the database, no matter what the attackers already know or wish to learn. Still, there is no practical system applying differential privacy algorithms for clustering points on real databases. This paper describes the construction of small coresets for computing k-means clustering of a set of points while preserving differential privacy. As a result, we give the first k-means clustering algorithm that is both differentially private, and has an approximation error that depends sub-linearly on the data's dimension d. Previous results introduced errors that are exponential in d. We implemented this algorithm and used it to create differentially private location data from GPS tracks. Specifically our algorithm allows clustering GPS databases generated from mobile nodes, while letting the user control the introduced noise due to privacy. We provide experimental results for the system and algorithms, and compare them to existing techniques. To the best of our knowledge, this is the first practical system that enables differentially private clustering on real data.

Duodenal adenocarcinoma is very rare among the general population. The diagnosis may be delayed until advanced stages, due to the subtle and nonspecific clinical manifestations of that rare pathology. Abdominal pain, upper gastrointestinal bleeding, weight loss and biliary obstruction may be the main patient’s complaints. We present a very interesting case of an old patient with dementia, hospitalized with a clinical, laboratory and imaging state consistent with cholangitis. Conservative therapy with antibiotics and an urgent ERCP was held, during the procedure, the major papilla could not be identified due to distorted anatomy of the second and third parts of the duodenum. Torsion like appearance of the duodenum was observed. Consequentially, the patient biliary tract was drained by inserting an internal– external drain percutaneously. Following the external drainage, a successful gastroscopy was done, with successful exploration of the proximal duodenum, revealing the true cause of the bile duct obstruction; a large pedunculated polypoid mass (approx. 30 mm), in proximate to the major papilla was found as well as the distal pigtailed plastic stent with was inserted as mentioned during angiography. The mass diagnosed as duodenal adenocarcinoma in pathology. This unique case describes presentation of an aggressive rare duodenal cancer, mimicking biliary cholangitis distorting the local anatomy. Endoscopic exploration became feasible due to primary percutaneous drainage.

Signal and image processing have seen an explosion of interest in the last few years in a new form of signal/image characterization via the concept of sparsity with respect to a dictionary. An active field of research is dictionary learning: the representation of a given large set of vectors (e.g. signals or images) as linear combinations of only few vectors (patterns). To further reduce the size of the representation, the combinations are usually required to be sparse, i.e., each signal is a linear combination of only a small number of patterns. This paper suggests a new computational approach to the problem of dictionary learning, known in computational geometry as coresets. A coreset for dictionary learning is a small smart non-uniform sample from the input signals such that the quality of any given dictionary with respect to the input can be approximated via the coreset. In particular, the optimal dictionary for the input can be approximated by learning the coreset. Since the coreset is small, the learning is faster. Moreover, using merge-and-reduce, the coreset can be constructed for streaming signals that do not fit in memory and can also be computed in parallel. We apply our coresets for dictionary learning of images using the K-SVD algorithm and bound their size and approximation error analytically. Our simulations demonstrate gain factors of up to 60 in computational time with the same, and even better, performance. We also demonstrate our ability to perform computations on larger patches and high-definition images, where the traditional approach breaks down.

We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and $d\geq n$. E.g., adjacency matrix of a graph, web-links, social network, document-terms, or image-features matrices. Our streaming algorithm stores at most $\log n\cdot k^{O(1)}$ input points in memory. If the stream is distributed among $M$ machines, the running time reduces by a factor of $M$, while communicating a total of $M\cdot k^{O(1)}$ (sparse) input points between the machines. % Our main technical result is a deterministic algorithm for computing a sparse $(k,\epsilon)$-coreset, which is a weighted subset of $k^{O(1)}$ input points that approximates the sum of squared distances from the $n$ input points to every $k$ centers, up to $(1\pm\epsilon)$ factor, for any given constant $\epsilon>0$. This is the first such coreset of size independent of both $d$ and $n$. Existing algorithms use coresets of size at least polynomial in $d$, or project the input points on a subspace which diminishes their sparsity, thus require memory and communication $\Omega(d)=\Omega(n)$ even for $k=2$. Experimental results real public datasets shows that our algorithm boost the performance of such given heuristics even in the off-line setting. Open code is provided for reproducibility., Comment: 16 pages, 44 figures

Spatial impulses are derived for SAR models containing a spatial unit root. Analytical solutions are obtained for lateral space where the number of spatial units tends to infinity. Numerical solutions are obtained for finite regular lattices where edge-effects are shown to influence spatial impulses, and for irregular lattices. Monte Carlo simulation methods are used to compute critical values for spatial unit root tests in SAR models estimated from spatial cross-section data for regular and irregular lattices. We also compute critical SAC values for spatial cointegration tests for cross-section data that happen to be spatially nonstationary. We show that parameter estimates in spatially cointegrated models are ‘superconsistent’. RESUME On derive des impulsions spatiales de modeles SAR contenant une racine unite spatiale. On obtient des solutions analytiques pour l'espace lateral lorsque le nombre d'unites spatiales tend vers l'infini. On obtient des solutions numeriques pour des reseaux regulier...

In continuously operating robotic systems, efficient representation of the previously seen camera feed is crucial. Using a highly efficient compression coreset method, we formulate a new method for hierarchical retrieval of frames from large video streams collected online by a moving robot. We demonstrate how to utilize the resulting structure for efficient loop-closure by a novel sampling approach that is adaptive to the structure of the video. The same structure also allows us to create a highly-effective search tool for large-scale videos, which we demonstrate in this paper. We show the efficiency of proposed approaches for retrieval and loop closure on standard datasets, and on a large-scale video from a mobile camera., Hon Hai/Foxconn International Holdings Ltd., Lincoln Laboratory, Singapore-MIT Alliance for Research and Technology Center (Future Urban Mobility Project), United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051)

Given an image stream, our on-line algorithm will select the semantically-important images that summarize the visual experience of a mobile robot. Our approach consists of data pre-clustering using coresets followed by a graph based incremental clustering procedure using a topic based image representation. A coreset for an image stream is a set of representative images that semantically compresses the data corpus, in the sense that every frame has a similar representative image in the coreset. We prove that our algorithm efficiently computes the smallest possible coreset under natural well-defined similarity metric and up to provably small approximation factor. The output visual summary is computed via a hierarchical tree of coresets for different parts of the image stream. This allows multi-resolution summarization (or a video summary of specified duration) in the batch setting and a memory-efficient incremental summary for the streaming case., Singapore-MIT Alliance for Research and Technology Center (Future Urban Mobility Project), Foxconn International Holdings Ltd., Singapore. National Research Foundation, United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051), United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1031), National Science Foundation (U.S.) (Award IIS-1117178)

This paper describes a system that takes as input GPS data streams generated by users' phones and creates a searchable database of locations and activities. The system is called iDiary and turns large GPS signals collected from smartphones into textual descriptions of the trajectories. The system features a user interface similar to Google Search that allows users to type text queries on their activities (e.g., "Where did I buy books?") and receive textual answers based on their GPS signals. iDiary uses novel algorithms for semantic compression (known as coresets) and trajectory clustering of massive GPS signals in parallel to compute the critical locations of a user. Using an external database, we then map these locations to textual descriptions and activities so that we can apply text mining techniques on the resulting data (e.g. LSA or transportation mode recognition). We provide experimental results for both the system and algorithms and compare them to existing commercial and academic state-of-the-art. This is the first GPS system that enables text-searchable activities from GPS data., United States. Office of Naval Research (Grant ONR-MURI Award N00014-12-1-1000), Hon Hai/Foxconn International Holdings Ltd., Singapore-MIT Alliance for Research and Technology Center, Singapore. National Research Foundation, United States. Dept. of Defense. National Defense Science & Engineering Graduate Fellowship Program

We present an approach to position k servers (e.g. mobile robots) to provide a service to n independently moving clients; for example, in mobile ad-hoc networking applications where inter-agent distances need to be minimized, connectivity constraints exist between servers, and no a priori knowledge of the clients' motion can be assumed. Our primary contribution is an algorithm to compute and maintain a small representative set, called a kinematic coreset, of the n moving clients.We prove that, in any given moment, the maximum distance between the clients and any set of k servers is approximated by the coreset up to a factor of (1 ± ε), where ε > 0 is an arbitrarily small constant. We prove that both the size of our coreset and its update time is polynomial in k log(n)/ε. Although our optimization problem is NP-hard (i.e., takes time exponential in the number of servers to solve), solving it on the small coreset instead of the original clients results in a tractable controller. The approach is validated in a small scale hardware experiment using robot servers and human clients, and in a large scale numerical simulation using thousands of clients., Micro Autonomous Consortium Systems and Technology (United States. Army Research Laboratory (Grant W911NF-08-2-0004)), United States. Air Force (Contract FA8721-05-C-0002)