On Low-rank Trace Regression under General Sampling Distribution

A growing number of modern statistical learning problems involve estimating a large number of parameters from a (smaller) number of noisy observations. In a subset of these problems (matrix completion, matrix compressed sensing, and multi-task learning) the unknown parameters form a high-dimensional matrix B*, and two popular approaches for the estimation are convex relaxation of rank-penalized regression or non-convex optimization. It is also known that these estimators satisfy near optimal error bounds under assumptions on rank, coherence, or spikiness of the unknown matrix. In this paper, we introduce a unifying technique for analyzing all of these problems via both estimators that leads to short proofs for the existing results as well as new results. Specifically, first we introduce a general notion of spikiness for B* and consider a general family of estimators and prove non-asymptotic error bounds for the their estimation error. Our approach relies on a generic recipe to prove restricted strong convexity for the sampling operator of the trace regression. Second, and most notably, we prove similar error bounds when the regularization parameter is chosen via K-fold cross-validation. This result is significant in that existing theory on cross-validated estimators do not apply to our setting since our estimators are not known to satisfy their required notion of stability. Third, we study applications of our general results to four subproblems of (1) matrix completion, (2) multi-task learning, (3) compressed sensing with Gaussian ensembles, and (4) compressed sensing with factored measurements. For (1), (3), and (4) we recover matching error bounds as those found in the literature, and for (2) we obtain (to the best of our knowledge) the first such error bound. We also demonstrate how our frameworks applies to the exact recovery problem in (3) and (4).Comment: 32 pages, 1 figur

On Worst-case Regret of Linear Thompson Sampling

In this paper, we consider the worst-case regret of Linear Thompson Sampling (LinTS) for the linear bandit problem. \citet{russo2014learning} show that the Bayesian regret of LinTS is bounded above by $\widetilde{\mathcal{O}}(d\sqrt{T})$ where $T$ is the time horizon and $d$ is the number of parameters. While this bound matches the minimax lower-bounds for this problem up to logarithmic factors, the existence of a similar worst-case regret bound is still unknown. The only known worst-case regret bound for LinTS, due to \cite{agrawal2013thompson,abeille2017linear}, is $\widetilde{\mathcal{O}}(d\sqrt{dT})$ which requires the posterior variance to be inflated by a factor of $\widetilde{\mathcal{O}}(\sqrt{d})$. While this bound is far from the minimax optimal rate by a factor of $\sqrt{d}$, in this paper we show that it is the best possible one can get, settling an open problem stated in \cite{russo2018tutorial}. Specifically, we construct examples to show that, without the inflation, LinTS can incur linear regret up to time $\exp(\Omega(d))$. We then demonstrate that, under mild conditions, a slightly modified version of LinTS requires only an $\widetilde{\mathcal{O}}(1)$ inflation where the constant depends on the diversity of the optimal arm

Modeling a four-layer location-routing problem

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations

Studying the relation between organizational justice and organizational commitment among the librarians of Khouzestan province ministry of science academic libraries

This research is designed to study the relation between organizational justice and organizational commitment among the librarians working in the academic libraries of Khouzestan province universities of ministry of science. The statistic population includes all the managers and librarian employees working in the selected libraries in the year 2013 (160 persons), among whom 133 persons have been asked to fill the 1993 Moorman’s survey of organizational justice and 1990 Meyer’s survey of organizational commitment. This is a correlational type study, carried out with a descriptive method. To analyze the relation between the variables, Pearson’s correlation coefficient and multiple-regression tests were used. In the end, among different factors of organizational justice, only the obtained mean of procedural justice was measured less than the average. And, the overall mean of organizational justice was measured just a little short of the average. Among different factors and elements of organizational commitment (affective, normative, continuance) the obtained results of continuance commitment is quite low. Yet, the overall mean of organizational commitment is higher than the average. There is a significant and positive relation between organizational justice and organizational commitment. Finally, among different factors of organizational justice, interactional justice can be more relied upon to assess the organizational commitment of the staff working in the studied libraries

Studying the relation between organizational justice and organizational commitment among the librarians of Khouzestan province ministry of science academic libraries

This research is designed to study the relation between organizational justice and organizational commitment among the librarians working in the academic libraries of Khouzestan province universities of ministry of science. The statistic population includes all the managers and librarian employees working in the selected libraries in the year 2013 (160 persons), among whom 133 persons have been asked to fill the 1993 Moorman’s survey of organizational justice and 1990 Meyer’s survey of organizational commitment. This is a correlational type study, carried out with a descriptive method. To analyze the relation between the variables, Pearson’s correlation coefficient and multiple-regression tests were used. In the end, among different factors of organizational justice, only the obtained mean of procedural justice was measured less than the average. And, the overall mean of organizational justice was measured just a little short of the average. Among different factors and elements of organizational commitment (affective, normative, continuance) the obtained results of continuance commitment is quite low. Yet, the overall mean of organizational commitment is higher than the average. There is a significant and positive relation between organizational justice and organizational commitment. Finally, among different factors of organizational justice, interactional justice can be more relied upon to assess the organizational commitment of the staff working in the studied libraries

Studying the relation between organizational justice and organizational commitment among the librarians of Khouzestan province ministry of science academic libraries

This research is designed to study the relation between organizational justice and organizational commitment among the librarians working in the academic libraries of Khouzestan province universities of ministry of science. The statistic population includes all the managers and librarian employees working in the selected libraries in the year 2013 (160 persons), among whom 133 persons have been asked to fill the 1993 Moorman’s survey of organizational justice and 1990 Meyer’s survey of organizational commitment. This is a correlational type study, carried out with a descriptive method. To analyze the relation between the variables, Pearson’s correlation coefficient and multiple-regression tests were used. In the end, among different factors of organizational justice, only the obtained mean of procedural justice was measured less than the average. And, the overall mean of organizational justice was measured just a little short of the average. Among different factors and elements of organizational commitment (affective, normative, continuance) the obtained results of continuance commitment is quite low. Yet, the overall mean of organizational commitment is higher than the average. There is a significant and positive relation between organizational justice and organizational commitment. Finally, among different factors of organizational justice, interactional justice can be more relied upon to assess the organizational commitment of the staff working in the studied libraries

Perception of the Characteristics of External Environment of Organizations and Its Effect on Managers’ Environmental Scanning in Using Information Resources

Abstract: Purpose: The purpose of the present study is to investigate the characteristics of external environment of companies in the second industrial area of Ahvaz and its effect on managers\u27 environmental scanning behavior in using information resources. Method: An analytic survey method is used to analyze the relationship between variables. Findings: The findings showed that managers\u27 perception of various external environment is influenced by variability factors (economic sector, M=3.96), complexity (economic sector, M=3.77) and importance (customers\u27 sector, M=4.38). also the findings showed that managers\u27 environmental scanning can match managers\u27 perceived characteristics of various sectors of external environment, and from this aspect, they do the greatest scanning in economic environmental sector (M=7.4). The highest perceived strategic uncertainty (M=33.239) and environmental uncertainty (M=7.73) belonged to economic sector. Testing research hypotheses proved that managers\u27 perceived strategic uncertainty and environmental uncertainty from environmental sectors of companies has a direct relationship with environmental sectors in those parts; and there is a direct and significant relationship between perceived environmental uncertainty and the frequency with which information resources is used in environmental scanning

Presented a dynamic model with project management for successful implementation of continuous improvement

Every year new words are born in the field of project management and continuous improvement. Some words refer to the Science Foundations of Strategic Management Accounting perspective and some simply grandiose and mouth filling, the promotional aspects are management consulting firms. Often in the Project Management, unaware of what is transposition of these systems, one can achieve improved competitiveness or perhaps chose to tinker purpose is achieved. Everything we offer in this article will aim to provide using a dynamic model for the continuous improvement of project management in line with the above objectives. Project management offices of various organizations are documented and analyzed. Organizational development and project management offices to the events, tensions and changes were separated. This article based on empirical evidence suggests that project management can improve Mstmrmy leaving behind the traditional theory of firm boundaries based on project management as part of the historical process within an organization is understood

Presented a dynamic model with project management for successful implementation of continuous improvement

Every year new words are born in the field of project management and continuous improvement. Some words refer to the Science Foundations of Strategic Management Accounting perspective and some simply grandiose and mouth filling, the promotional aspects are management consulting firms. Often in the Project Management, unaware of what is transposition of these systems, one can achieve improved competitiveness or perhaps chose to tinker purpose is achieved. Everything we offer in this article will aim to provide using a dynamic model for the continuous improvement of project management in line with the above objectives. Project management offices of various organizations are documented and analyzed. Organizational development and project management offices to the events, tensions and changes were separated. This article based on empirical evidence suggests that project management can improve Mstmrmy leaving behind the traditional theory of firm boundaries based on project management as part of the historical process within an organization is understood