High-dimensional learning of linear causal networks via inverse covariance estimation

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l_2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.Comment: 41 pages, 7 figure

Edge detection using fuzzy switch

This paper is to switch various edge filters via a fuzzy approach

Sinusoidal response of a second-order digital filter with two’s complement arithmetic

In this paper, results of the sinusoidal response case are presented. It is found that the visual appearance of the trajectory of the sinusoidal response case is much richer than that of the autonomous and step response cases. Based on the state space technique, the state vectors to be periodic are investigated. The set of initial conditions and the necessary conditions on the filter parameters are also derived. When overflow occurs, the system is nonlinear. If the corresponding symbolic sequences are periodic, some trajectory patterns are simulated. Since the state space technique is not sufficient to efficiently derive the sets of initial conditions and the necessary conditions on the filter parameters, a frequency-domain technique is employed to figure out the set of initial conditions. When the symbolic sequences are aperiodic, an elliptical fractal pattern or random-like chaotic pattern is found

Effect of non-polynomial input to a switching circuit

In this paper, the validity of the state-space averaging method is analyzed. We assume that the state-space piecewise method is an exact model for a fast switching circuit. Based on this model, we compute the error predicted by the state-space averaging method. It is found that the error for a polynomial input is bounded by two polynomials with the same order as that of the input. And the percentage error is bounded by a constant. Hence, if the acceptable level is within that constant, then the state-space averaging method can be applied. Similar analysis is carried out on a non-polynomial input. A sinusoidal function is chosen because of its wide applications on AC circuits. Although a similar result is obtained, the percentage error for the sinusoidal input is much greater than that of the polynomial input. Hence, the state-space averaging method may not be so good for the AC analysis

Nonstationary Discrete Choice

This paper develops an asymptotic theory for time series discrete choice models with explanatory variables generated as integrated processes and with multiple choices and threshold parameters determining the choices. The theory extends recent work by Park and Phillips (2000) on binary choice models. As in this earlier work, the maximum likelihood (ML) estimator is consistent and has a limit theory with multiple rates of convergence (n^{3/4} and n^{1/4}) and mixture normal distributions where the mixing variates depend on Brownian local time as well as Brownian motion. An extended arc sine limit law is given for the sample proportions of the various choices. The new limit law exhibits a wider range of potential behavior that depends on the values taken by the threshold parameters.Brownian motion, Brownian local time, Discrete choice model, Dual convergence rates, Extended arc sine laws, Integrated time series, Maximum likelihood estimation, Threshold parameters

Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach

We apply a discrete choice approach to model the empirical behavior of the Federal Reserve in changing the federal funds target rate, the benchmark of short term market interest rates in the US. Our methods allow the explanatory variables to be nonstationary as well as stationary. This feature is particularly useful in the present application as many economic fundamentals that are monitored by the Fed and are believed to affect decisions to adjust interest rate targets display some nonstationarity over time. The empirical model is determined using the PIC criterion (Phillips and Ploberger, 1996; Phillips, 1996) as a model selection device. The chosen model successfully predicts the majority of the target rate changes during the time period considered (1985-2001) and helps to explain strings of similar intervention decisions by the Fed. Based on the model-implied optimal interest rate, our findings suggest that there a lag in the Fed's reaction to economic shocks and that the Fed is more conservative in raising interest rates than in lowering rates.Extended arc sine laws, Federal funds target rate, Interest rate, Monetary policy, Nonstationary discrete choice

Stabilization of (L,M) shift invariant plant

In this paper, a lifting technique is employed to realize a single input single output linear (L,M) shift invariant plant as a filter bank system. Based on the filter bank structure, a controller is designed so that the aliasing components in the control loop are cancelled and the loop gain becomes a time invariant transfer function. Pole placement technique is applied to stabilize the overall system and ensure the causality of the filters in the controller. An example on the control of a linear (L,M) shift invariant plant with simulation result is illustrated. The result shows that our proposed algorithm is simple and effective