Enjoy the setting sun with our talented Chaumette staffer and saxophonist Gerry Huggins! Gerry will play smooth jazz tunes in the evenings on our North Gallery, overlooking the rolling hills of Ste. Genevieve, and guests are welcome to join us for dinner at our Grapevine Grill or enjoy a glass of wine on the patio from our Tasting Bar. Live entertainment is complimentary, as always. Restaurant reservations: 573-747-1000. Hope to see you soon!
Performer: Gerry Huggins Genre: Jazz/blues/RB/soul Listen to his music here:
https://www.tradebit.com/filedetail.php/890309-gerry-huggins
Website:
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Artist Bio: At age nine, Gerry Huggins began to explore the musical world with his saxophone. His talents with his sax won him the Outstanding Musician award in senior year of high school. Huggins attended Cal State University and received a BA in Communications. While studying, he continued playing his saxophone at Bakersfield College. This earned him two Most Outstanding Musician awards in the Bakersfield College Jazz Ensemble. In addition, he won two Outstanding Soloist awards for his appearances at the Fullerton College Jazz festival. His love for music turned professional during the mid 90s. He was invited to record with the local band, "The Pleasure Merchants" in their sophomore album, "Rhyme or Reason". Following that, he began playing for a variety of local bands, including "Thee Majestics", "T.O.S.B (The Old School Band)", and "The Rhythm Kings". After collaborating with keyboardist Darnell Gholston, he realized that his true passion was smooth jazz and RB. Funk, jazz and old school styles are also among the genres Huggins exceeds in. His technique also can stretch from classical to big band. His debut album, "Ocean Breeze" was released in 2002; only to be followed by "A Very Special Christmas" in 2005 and "From the Heart" in 2007. Huggins is currently working on new material and hopefully will be released in the near future. Huggins continues to freelance in the Southern California area. He has a son, and resides in Bakersfield, CA.
Celebrate Volksweston with a delectable blue and white signature Volkswagon or Love Bug Cupcake. These full-sized vanilla and chocolate cupcakes are only $1.99/each, $10.99 for a 6-pack or $19.99/dozen! Feel free to call us at (816) 386-2345 to reserve your cupcakes as they’re only available while supplies last. No reservations are needed for our standard wine tasting - just stop by during business hours to tantalize your taste buds!
This should look familiar, we are just replacing limits/expectations/etc with their empirical counterparts.
can be written as
\hat{f}(x) = \frac{1}{nh} \sum_{i=1}^n w \left(\frac{x-X_i}{h}\right)
w(x) = \left\{ \begin{array}{lr} 1/2 if |x| < 1 \\ 0 else\end{array}\right.
In general you can can write a kernel smoother as:
\hat{f}(x) = \frac{1}{nh} \sum_{i=1}^n K\left(\frac{x-X_i}{h}\right)
where \int K(x) dx =1 (this guarantees that \int \hat{f}(x) dx = 1 ) and h is the bandwidth.
http://longor.public.iastate.edu/Stat516S13/slides/04.smoothing1.pdf
We often care about things like MSE:
MSE(x) = \mathbb{E}\left[\left(\hat{f}(x) - f(x)\right)^2\right]
=\left(\mathbb{E}[\hat{f}(x)] - f(x)\right)^2 + {\rm Var}(\hat{f}(x))
E_{\hat{F}}[Y|X=x_0] = {\rm a.v.e.} \{ y_i; x_i = x_0\}
If the values of x_i are categorical we can estimate this directly.
If not we need to "borrow strength"
You've seen this before for linear regression
Define \{W_i(x)\}_{i=1}^{n} for each x and let
s(x) = \sum_{i=1}^n W_i(x) y_i
http://www.biostat.jhsph.edu/~ririzarr/Teaching/754/
E[ Y | X ] = \int y f_{X,Y}(x,y) \, dy / f_X(x)
s(x) = \frac{ n^{-1}\sum_{i=1}^n K\left( \frac{x - x_i}{h} \right) y_i } { n^{-1}\sum_{i=1}^n K\left ( \frac{ x - x_i }{h} \right)}
Again we are basically just taking integrals and replacing them with sums. Noticing a theme here? Write down the theoretical parameter you are trying to estimate and then substitute empirical analogs.
Bias(x) = \int K(z) (f(x-hz) - f(z))dz
Var(x) = n^{-1} \int \frac{1}{h^2} K\left(\frac{x-y}{h}\right)^2 f(y)dy - n^{-1} \left(\int \frac{1}{h}K\left(\frac{x-y}{h}\right)f(y)dy \right)^2
Assume h = h_n \rightarrow 0 with nh_n \rightarrow 0 . If this is true then bias/variance go to zero as n\rightarrow \infty .
You can asymptotically minimize MSE(X) by solving \frac{\partial}{\partial h} MSE(x) = 0
You get something like this:
h_{opt} = n^{-1/5} \left(\frac{f(x)\int K^2(z)dz}{(f''(x)^2 (\int z^2 K(z)dz)^2)}\right)^{1/5}
Derivation:
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X_1, \ldots, X_n \sim f(x_1,\ldots,x_d)
We can estimate a multivariate smoother
\hat{f}(x) = \frac{1}{nh^d} \sum_{i=1}^n K\left(\frac{x_i-X_i}{h}\right)
wher the kernel K(\cdot) is now a function on a d-dimensional vector satisfying
K(u) \geq 0 , \int_{\mathbb{R}^d} K(u)du = 1 , \int_{\mathbb{R}^d}uK(u)du = 0 and \int_{\mathbb{R}^d} uu^T K(u)du = I_d
You must be 21 to attend!
ID's will be checked at the door.
Event URL: https://www.facebook.com/events/1208437939221935
Playing your favorite Country Tunes.
Live Music with Ramblin Pan and Guest
Event website: windywine.com
Playing Classic Rock and today's favorites.
Bid on local vendors goods and support the veterans!
$35 pp includes all supplies needed, with step by step instructions,light snacks, and a beverage of your choice.You will be paintinga Kansas City Chiefs canvas painting.Must register prepay.
NonRefundable.
Instructor:Chrissy
$20 pp includes step by step instructions.Relieve stress and strengthencoremuscles in a judgement free environment.Must register.
$30 buys the class, supplies, and a glass of wine or beer! This session we are painting the northern lights.
Wine Glass Fridays - Painting Event
If we consider spike firing as a
stochastic
process we can think of the firing rate also as the probability density of finding a spike at a certain instance of time. In this picture, is the rate of the underlying Poisson process that generates the spikes; cf. Section
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. Stochastic rate models are therefore on the border line between analog rate models and noisy spiking neuron models. The main difference is that stochastic spiking neuron models such as the Spike Response Model with escape noise (cf. Section
5.3
) allows us to include refractoriness whereas a Poisson model does not (
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).
A stochastic rate model in continuous time is defined by an inhomogeneous Poisson process. Spikes are formal events characterized by their firing time t _{ j } ^{ (f) } where j is the index of the neuron and f counts the spikes. At each moment of time spikes are generated with rate ( t ) which depends on the input. It is no longer possible to calculate the input from a rate equation as in Eq.( 5.127 ) since the input consists now of spikes which are point events in time. We set
In order to illustrate the relation with the deterministic rate model of Eq.( 5.128 ), we discretize time in steps of length t = 1/ where is the maximum firing rate. In each time step the stochastic neuron is either active ( S _{ i } = + 1) or quiescent ( S _{ i } = 0). The two states are taken stochastically with a probability which depends continuously upon the input h _{ i } . The probability that a neuron is active at time t + t given an input h _{ i } at time t is
Closely related to the stochastic point of view is the notion of the rate as the average activity of a population of equivalent neurons. `Equivalent' means that all neurons have identical connectivity and receive the same type of input. Noise, however, is considered to be independent for each pair of neurons so that their response to the input can be different. We have seen in Section
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that we can define a `rate', if we take a short time window
t
, count the number of spikes (summed over all neurons in the group) that occur in an interval
t
...
t
+
t
and divide by the number of neurons and
t
. In the limit of
N
and
t
0 (in this order), the activity
A
is an analog variable which varies in continuous time,
Let us assume that we have several groups of neurons. Each group l contains a large number of neurons and can be described by its activity A _{ l } . A simple phenomenological model for the interaction between different groups is
We will see later in Chapter
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, that Eq.(
5.137
) is indeed a correct description of the fixed point of interacting populations of neurons, that is, if all activity values
A
_{
k
}
are, apart from fluctuations constant. As mentioned in Chapter
1.4
, the interpretation of the rate as a population activity is not without problems. There are hardly ensembles which would be large enough to allow sensible averaging and, at the same time, consist of neurons which are strictly equivalent in the sense that the internal parameters and the input is identical for all the neurons belonging to the same ensemble. On the other hand, neurons in the cortex are often arranged in groups (columns) that are roughly dealing with the same type of signal and have similar response properties. We will come back to the interpretation of Eq.(
5.137
) as a population activity in Chapter
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.