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A couple of weeks ago, a colleague and I went on a trip to Vienna, Austria to deliver a keynote to a state-funded innovation agency to discuss entrepreneurship and the role of mentoring. One of the key points that came out of that discussion was the role of accelerators and the state of growth funding in Europe’s central hub – Berlin.

It seems that every few months, there is a new accelerator or incubator popping up. There are now over 10 industry-focused accelerators/incubators in Berlin alone scooping up startups in healthcare, hardware, media/publishing, ed-tech, enterprise SaaS, real estate, e-commerce, and even rail logistics. While many startups are finishing classes (accelerators) or much longer programs (incubators), there are very few able to raise substantial seed (growth) rounds or Series A rounds.

To conjecture why this might be the case, it is important to start with a critical distinction between the accelerator class model and the incubator model in Germany. The former is usually three months long. Its usually modeled after TechStars with funding of anywhere from 15k to 25k for equity ranging from 5 percent to 8 percent of equity. The latter is much longer, usually is more hands-on, and is an extension of a company or fund (more about this later). The biggest difference in the accelerator model in Germany vs. in the US is that while US accelerator (TechStars network/YC) startups have automatic access to convertible notes (100k/80k), German accelerators do not, which poses a growth challenge for companies after their jumpstart.

Lets briefly look at the state funding environment. A recent report produced by the Berlin Department of Senate showed a plethora of funding options. If you look much closer, while there are one or two university affiliated grants, most are debt financing options or subsidies with stringent working capital requirements. This underscores much of the EU landscape – aversion to risk. A recent post by Inge Geeerdens sheds some light on this issue.

More important is how the private sector – German VCs – view startups and what they are willing to fund. While Rocket Internet’s incubation model is an outlier, it has gained precedence and sheds some insights on how much risk VCs here will take. While we are in 2014, this blog post written two years ago from Jason Jozefak, a Germany-based venture capitalist, is still very relevant. Martin Varsavsky summarized it succinctly in this post where he states “funding is more complicated in Berlin because Germans have a natural aversion to risk, which in turn makes it hard for their financial system to find a good way to consistently finance failures.”

To control for risk, the trend in Germany is to micromanage ventures in an incubator-type model, .i.e, Atlantic Ventures, Epic, Team Europe, Project A, or HitFoxGroup. And to that effect, some of them have managed to hack growth with portfolio companies that are tightly structured on business models in the US.

Of course times are changing and London VCs want in on some of the Berlin action. But it’s Europe after all, and startups need to show growth with limited seed funding to gain follow-on rounds and eventually prove their Series A worth.

Perhaps US-based funds will come to the rescue.

You're reading __Post Accelerator And Growth Funding In Berlin, Series A Crunch__

## 10 Ways To Develop A Growth Mindset In Business

Most of us enjoy pleasure when our thoughts come to fruition. We are even more pleased when the thoughts have an effect by enhancing motivation, productivity or innovation, among other regions. The spread of the idea may gain several, but that prevalence may also change and distort the first.

A growth mindset is “the belief that an individual’s most basic abilities and skills can be developed through dedication and hard work—brains and talent are just the starting point.”

A fixed mindset is “the belief that an individual’s basic abilities and skills, their intelligence and their talents, are just fixed traits.”

Adopting a growth mindset can supercharge your wellbeing and growth.

Here are 10 ways to develop a growth mindset in business 1. Be 100 percent accountableAlso read: How to Calculate Your Body Temperature with an iPhone Using Smart Thermometer

2. Do not be concerned with what others havePreventing jealousy is basically important once you’re attempting to become more focused, leading and driven. Focusing on which others have and what they’re doing sets expectations which just slow you down and draw attention away from your objective.

3. Become an expert in your fieldI meet many so-called”headliners,” individuals who skim the surface. In a world fueled by bogus information, Photoshop’ed social posts and other illusions, it is essential to develop into a specialist.

Try to become really great at everything you doso great that everyone needs your services. Stand out according to your specialization.

4. Don’t focus on your failuresAs soon as we learn that we ought to work on our flaws, we have a tendency to believe we will need to continue to our failures.

But focusing on your own failures provides detractors a lot of leverage. Rather, maintain and learn from the failures and focus on growing and learning from the own mistakes and daily improve personal development.

5. Do the work and put in the timeAlso read: What Is Gaming In Metaverse? 7 Best Metaverse Games To Try (#1 is played by millions of YouTubers)

6. Do what you love for the people who love what you doOne of my favourite expressions is,”You have to be purpose-driven doing exactly what you love for people who adore what you do.” Discovering your goal is as critical as finding your market.

You may bring a whole lot more value and experience to people who want you, and you’ll have much more fun delivering your services and products.

7. Don’t focus on moneyBusiness leaders who concentrate solely on cash are not completely satisfied, and frequently lose their clients. Rather, care about producing value. You need clients to say how pleased they’re about your services and products.

You need employees to say just how good it’s to work to you and just how much they learn from you. Concentrate on producing fans through value creation.

8. Achieve your outcomes quicklyDon’t be obsessed with perfection. Rather, be quick. Getting someplace first has more significance than being ideal but continue.

This first-mover benefit is essential for growth. Develop a desire to fail regularly and fast, developing your services and products fast and better aligned with the requirements of your clients.

9. Be grateful for what you haveBe thankful for everything you have today. Be thankful for what you are likely to attain. Be thankful for what you do not have.

Also read: Best CRM software for 2023

10. Become self-aware and understand your purposeIf you would like to be successful in life, you have to be aware of that your objective. If you would like a company growth mindset, then you have to become self-aware and comprehend that your objective.

Self-awareness has the capability to align your will and humility, which brings people to you through your objective.

Growth mindset is your belief that skills and skills can be made better and that creating these is the aim of your own actions.

Construct a culture where all workers are encouraged and permitted to develop expansion mindsets for themselves–benefit development.

Emphasize that failures are chances rather than threats. Leaders will need to promote and challenge workers to become brave and courageous.

An expansion mindset is an ongoing belief that progress is possible and failures are chances to learn. It’s a lot bigger than the restricted purpose of enhancing earnings.

Growing mindset is a frame of mind. Leaders can positively assist people in embracing growth mindsets by fostering a culture supporting specific behaviours and practices. Organizations and individuals may have increase mindsets.

A growth mindset isn’t unbounded. Just because you set your head to something does not mean you’re able to do anything. You need to work at it, so begin by implementing these ten measures and start to live with intention.

## A Comprehensive Guide To Time Series Analysis And Forecasting

This article was published as a part of the Data Science Blogathon.

Time Series Analysis and Forecasting is a very pronounced and powerful study in data science, data analytics and Artificial Intelligence. It helps u changing time. For example, let us suppose you have visited a clinic due to some chest pain and want to get an (ECG) test done to see if your heart is healthy functioning. The ECG graph produced is a time-series data where your Heart Rate Variability (HRV) with respect to time is plotted, analysing which the doctor can suggest crucial measures to take care of your heart and reduce the risk of stroke or heart attacks. Time Series is used widely in healthcare analytics, geospatial analysis, weather forecasting, and to forecast the future of data that changes continuously with time!

What is Ti ries Analysis in Machine Learning?Time-series analysis is the process of extracting useful information from time-series data to forecast and gain insights from it. It consists of a series of data that varies with time, hence continuous and non-static in nature. It may vary from hours to minutes and even seconds (milliseconds to microseconds). Due to its non-static and continuous nature, working with time-series data is indeed difficult even today!

As time-series data consists of a series of observations taken in sequences of time, it is entirely non-static in nature.

Time Series – Analysis Vs. ForecastingTime series data analysis is the scientific extraction of useful information from time-series data to gather insights from it. It consists of a series of data that varies with time. It is non-static in nature. Likewise, it may vary from hours to minutes and even seconds (milliseconds to microseconds). Due to its continuous and non-static nature, working with time-series data is challenging!

As time-series data consists of a series of observations taken in sequences of time, it is entirely non-static in nature.

Time Series Analysis and Time Series Forecasting are the two studies that, most of the time, are used interchangeably. Although, there is a very thin line between this two. The naming to be given is based on analysing and summarizing reports from existing time-series data or predicting the future trends from it.

Thus, it’s a descriptive Vs. predictive strategy based on your time-series problem statement.

In a nutshell, time series analysis is the study of patterns and trends in a time-series data frame by descriptive and inferential statistical methods. Whereas, time series forecasting involves forecasting and extrapolating future trends or values based on old data points (supervised time-series forecasting), clustering them into groups, and predicting future patterns (unsupervised time-series forecasting).

The Time Series IntegrantsAny time-series problem or data can be broken down or decomposed into several integrants, which can be useful for performing analysis and forecasting. Transforming time series into a series of integrants is called Time Series Decomposition.

A quick thing worth mentioning is that the integrants are broken further into 2 types-

1. Systematic — components that can be used for predictive modelling and occur recurrently. Level, Trend, and Seasonality come under this category.

2. Non-systematic — components that cannot be used for predictive modelling directly. Noise comes under this category.

The original time series data is hence split or decomposed into 5 parts-

1. Level — The most common integrant in every time series data is the level. It is nothing but the mean or average value in the time series. It has 0 variances when plotted against itself.

2. Trend — The linear movement or drift of the time series which may be increasing, decreasing or neutral. Trends are observable over positive(increasing) and negative(decreasing) and even linear slopes over the entire range of time.

3. Seasonality — Seasonality is something that repeats over a lapse of time, say a year. An easy way to get an idea about seasonality- seasons, like summer, winter, spring, and monsoon, which come and go in cycles throughout a specified period of time. However, in terms of data science, seasonality is the integrant that repeats at a similar frequency.

Note — If seasonality doesn’t occur at the same frequency, we call it a cycle. A cycle does not have any predefined and fixed signal or frequency is very uncertain, in terms of probability. It may sometimes be random, which poses a great challenge in forecasting.

4. Noise — A irregularity or noise is a randomly occurring integrant, and it’s optional and arrives under observation if and only if the features are not correlated with each other and, most importantly, variance is the similar across the series. Noise can lead to dirty and messy data and hinder forecasting, hence noise removal or at least reduction is a very important part of the time series data pre-processing stage.

5. Cyclicity — A particular time-series pattern that repeats itself after a large gap or interval of time, like months, years, or even decades.

The Time Series Forecasting ApplicationsTime series analysis and forecasting are done on automating a variety of tasks, such as-

Weather Forecasting

Anomaly Forecasting

Sales Forecasting

Stock Market Analysis

ECG Analysis

Risk Analysis

and many more!

Time Series Components CombinatoricsA time-series model can be represented by 2 methodologies-

The Additive Methodology —

When the time series trend is a linear relationship between integrants, i.e., the frequency (width) and amplitude(height) of the series are the same, the additive rule is applied.

Additive methodology is used when we have a time series where seasonal variation is linear or constant over timestamps.

It can be represented as follows-

y(t) or x(t) = level + trend + seasonality + noise

where the model y(multivariate) or x(univariate) is a function of time t.

The Multiplicative Methodology —

When the time series is not a linear relationship between integrants, then modelling is done following the multiplicative rule.

The multiplicative methodology is used when we have a time series where seasonal variation increases with time — which may be exponential or quadratic.

It is represented as-

y(t) or x(t)= Level * Trend * Seasonality * Noise

Deep-Dive into Supervised Time-Series ForecastingSupervised learning is the most used domain-specific machine learning, and hence we will focus on supervised time series forecasting.

This will contain various detailed topics to ensure that readers at the end will know how to-

Load time series data and use descriptive statistics to explore it

Scale and normalize time series data for further modelling

Extracting useful features from time-series data (Feature Engineering)

Checking the stationarity of the time series to reduce it

ARIMA and Grid-search ARIMA models for time-series forecasting

Heading to deep learning methods for more complex time-series forecasting (LSTM and bi-LSTMs)

So without further ado, let’s begin!

Load Time Series Data and Use Descriptive Statistics to Explore itFor the easy and quick understanding and analysis of time-series data, we will work on the famous toy dataset named ‘Daily Female Births Dataset’.

Get the dataset downloaded from here.

Importing necessary libraries and loading the data –

import numpy import pandas import statmodels import matplotlib.pyplot as plt import seaborn as sns data = pd.read_csv(‘daily-total-female-births-in-cal.csv’, parse_dates = True, header = 0, squeeze=True) data.head()This is the output we get-

1959–01–01 35 1959–01–02 32 1959–01–03 30 1959–01–04 31 1959–01–05 44 Name: Daily total female births in California, 1959, dtype: int64Note —Remember, it is required to use ‘parse_dates’ because it converts dates to datetime objects that can be parsed, header=0 which ensures the column named is stored for easy reference, and squeeze=True which converts the data frame of single object elements into a scalar.

Exploring the Time-Series Data –

print(data.size) #output-365(a) Carry out some descriptive statistics —

print(data.describe())Output —

count 365.000000 mean 41.980822 std 7.348257 min 23.000000 25% 37.000000 50% 42.000000 75% 46.000000 max 73.000000(b) A look at the time-series distribution plot —

pyplot.plot(series) pyplot.show() Scale and Normalize Time Series Data for Further ModellingA normalized data scales the numeric features in the training data in the range of 0 and 1 so that gradient descent and loss optimization is fast and efficient and converges quickly to the local minima. Interchangeably known as feature scaling, it is crucial for any ML problem statement.

Let’s see how we can achieve normalization in time-series data.

For this purpose, let’s pick a highly fluctuating time-series data — the minimum daily temperatures data. Grab it here!

Let’s have a look at the extreme fluctuating nature of the data —

Source-DataMarket

To normalize a feature, Scikit-learn’s MinMaxScaler is too handy! If you want to generate original data points after prediction, an inverse_transform() function is also provided by this awesome built-in function!

Here goes the normalization code —

# import necessary libraries import pandas from sklearn.preprocessing import MinMaxScaler # load and sanity check the data data = read_csv(‘daily-minimum-temperatures-in-me.csv’, parse_dates = True, header = 0, squeeze=True, index_col=0) print(data.head()) #convert data into matrix of row-col vectors values = data.values values = values.reshape((len(values), 1)) # feature scaling scaler = MinMaxScaler(feature_range=(0, 1)) #fit the scaler with the train data to get min-max values scaler = scalar.fit(values) print(‘Min: %f, Max: %f’ % (scaler.data_min_, scaler.data_max_)) # normalize the data and sanity check normalized = scaler.transform(values) for i in range(5): print(normalized[i]) # inverse transform to obtain original values original_matrix= scaler.inverse_transform(normalized) for i in range(5): print(original_matrix[i])Let’s have a look at what we got –

See how the values have scaled!

Note — In our case, our data does not have outliers present and hence a MinMaxScaler solves the purpose well. In the case where you have an unsupervised learning approach, and your data contains outliers, it is better to go for standardization, which is more robust than normalization, as normalization scales the data close to the mean which doesn’t handle or include outliers leading to a poor model. Standardization, on the other hand, takes large intervals with a standard deviation value of 1 and a mean of 0, thus outlier handling is robust.

More on that here!

Extracting Useful Features from Time-Series Data (Feature Engineering)Framing data into a supervised learning problem simply deals with the task of handling and extracting useful features and discarding irrelevant features to make the model robust and cost-efficient.

We already know that supervised learning problems have 2 types of features — the independents (x) and dependent/target(y). Hence, how better the target value is achieved depends on how well we choose and engineer the independent features.

You must know by now that time-series data has two columns, timestamp, and its respective value. So, it is very self-explanatory that in the time series problem, the independent feature is time and the dependent feature is value.

Now let us look at what are the features that need to be engineered into these input and output values so that the inherent relationship between these two variables is established to make the forecasting as good as possible.

The features which are extremely important to model the relationship between the input and output variables in a time series are —

1. Descriptive Statistical Features — Quite straightforward as it sounds, calculating the statistical details and summary of any data is extremely important. Mean, Median, Standard Deviation, Quantiles, and min-max values. These come extremely handy while in tasks such as outlier detection, scaling and normalization, recognizing the distribution, etc.

2. Window Statistic Features — Window features are a statistical summary of different statistical operations upon a fixed window size of previous timestamps. There are, in general, 2 ways to extract descriptive statistics from windows. They are

(a) Rolling Window Statistics: The rolling window focuses on calculating rolling means or what we conventionally call Moving Average, and often other statistical operations. This calculates summary statistics (mostly mean) across values within a specific sliding window, and then we can assign these as features in our dataset.

Let, the mean at timestamp t-1 is x and t-2 be y, so we find the average of x and y to predict the value at timestamp t+1. The rolling window hence takes a mean of 2 values to predict the 3rd value. After that is done, the window shifts to the next set of values, and hence the mean is calculated for each window consisting of 2 values. We use rolling window statistics more often when the recent data is more important for forecasting and not previous data.

Let’s see how we can calculate moving or rolling average with a rolling window —

from pandas import DataFrame from pandas import concat df = DataFrame(data.values) tshifts = df.shift(1) rwin = tshifts.rolling(window=2) moving_avg = rwin.mean() joined_df = concat([moving_avg, df], axis=1) joined_df.columns = [‘mean(t-2,t-1)’, ‘t+1’] print(joined_df.head(5))Let’s have a look at what we got —

(b) Expanding Window Statistics: Almost similar to the rolling window, expanding windows takes into account an extra habit of extracting the predicted value as well as all the previous observations, each time it expands. This is beneficial when the previous data is equally important for forecasting as well as the recent data.

Let’s have a quick look at expanding window code-

window = tshifts.expanding() joined_df2 = concat([rwin.mean(),df.shift(-1)], axis=1) joined_df2.columns = ['mean', 't+1'] print(joined_df2.head(5))Let’s have a look at what we got -

3. Lag Features — Lag is simply predicting the value at timestamp t+1, provided we know the value at the previous timestamp, say, t-1. It’s simply distance or lag between two values at 2 different timestamps.

4. Datetime Features — This is simply the conversion of time into its specific components like a month, or day, along with the value of temperature for better forecasting. By doing this, we can gather specific information about the month and day at a particular timestamp for each record.

5. Timestamp Decomposition — Timestamp decomposition includes breaking down the timestamp into subset columns of timestamp for storing unique and special timestamps. Before Diwali or, say, Christmas, the sale of crackers and Santa-caps, fruit-cakes increases exponentially more than at other times of the year. So storing such a special timestamp by decomposing the original timestamp into subsets is useful for forecasting.

Time-series Data Stationary ChecksSo, let’s first digest what stationary time-series data is!

Stationary, as the term suggests, is consistent. In time-series, the data if it does not contain seasonality or trends is termed stationary. Any other time-series data that has a specific trend or seasonality, are, thus, non-stationary.

Can you recall, that amongst the two time-series data we worked on, the childbirths data had no trend or seasonality and is stationary. Whereas, the average daily temperatures data, has a seasonality factor and drifts, and hence, it’s non-stationary and hard to model!

Stationarity in time-series is noticeable in 3 types —

(a) Trend Stationary — This kind of time-series data possesses no trend.

(b) Seasonality Stationary — This kind of time-series data possesses no seasonality factor.

(c) Strictly Stationary — The time-series data is strictly consistent with almost no variance to drifts.

Now that we know what stationarity in time series is, how can we check for the same?

Vision is everything. A quick visualization of your time-series data at hand can give a quick eye review of whether the data can be stationary or not. Next in the line comes the statistical summary. A clear look into the summary statistics of the data like min, max, variance, deviation, mean, quantiles, etc. can be very helpful to recognize drifts or shifts in data.

Lets POC this!

So, we take stationary data, which is the handy childbirths data we worked on earlier. However, for the non-stationary data, let’s take the famous airline-passenger data, which is simply the number of airline passengers per month, and prove how they are stationary and non-stationary.

Case 1 — Stationary Proof

import pandas as pd import matplotlib.pyplot as plt data = pd.read_csv(‘daily-total-female-births.csv’, parse_dates = True, header = 0, squeeze=True) data.hist() plt.show()Output —

As I said, vision! Look how the visualization itself speaks that it’s a Gaussian Distribution. Hence, stationary!

More curious? Let’s get solid math proof!

X = data.values seq = round(len(X) / 2) x1, x2 = X[0:seq], X[seq:] meanx1, meanx2 = x1.mean(), x2.mean() varx1, varx2 = x1.var(), x2.var() print(‘meanx1=%f, meanx2=%f’ % (meanx1, meanx2)) print(‘variancex1=%f, variancex2=%f’ % (varx1, varx2))Output —

meanx1=39.763736, meanx2=44.185792 variancex1=49.213410, variancex2=48.708651The mean and variances linger around each other, which clearly shows the data is invariant and hence, stationary! Great.

Case 2— Non-Stationary Proof

import pandas as pd import matplotlib.pyplot as plt data = pd.read_csv(‘international-airline-passengers.csv’, parse_dates = True, header = 0, squeeze=True) data.hist() plt.show()Output —

The graph pretty much gives a seasonal taste. Moreover, it is too distorted for a Gaussian tag. Let’s now quickly get the mean-variance gaps.

X = data.values seq = round(len(X) / 2) x1, x2 = X[0:seq], X[seq:] meanx1, meanx2 = x1.mean(), x2.mean() varx1, varx2 = x1.var(), x2.var() print(‘meanx1=%f, meanx2=%f’ % (meanx1, meanx2)) print(‘variancex1=%f, variancex2=%f’ % (varx1, varx2))Output —

meanx1=182.902778, meanx2=377.694444 variancex1=2244.087770, variancex2=7367.962191Alright, the value gap between mean and variances are pretty self-explanatory to pick the non-stationary kind.

ARMA, ARIMA, and SARIMAX Models for Time-Series ForecastingA very traditional yet remarkable ‘machine-learning’ way of forecasting a time series is the ARMA (Auto-Regressive Moving Average) and Auto Regressive Integrated Moving Average Model commonly called ARIMA statistical models.

Other than these 2 traditional approaches, we have SARIMA (Seasonal Auto-Regressive Integrated Moving Average) and Grid-Search ARIMA, which we will see too!

So, let’s explore the models, one by one!

ARMA

The ARMA model is an assembly of 2 statistical models — the AR or Auto-Regressive model and Moving Average.

The Auto-Regressive Model estimates any dependent variable value y(t) at a given timestamp t on the basis of lags. Look at the formula below for a better understanding —

Here, y(t) = predicted value at timestamp t, α = intercept term, β = coefficient of lag, and, y(t-1) = time-series lag at timestamp t-1.

So α and β are the model estimators that estimate y(t).

The Moving Average Model plays a similar role, but it does not take the past predicted forecasts into account, as said earlier in rolling average. It rather uses the lagged forecast errors in previously predicted values to predict the future values, as shown in the formula below.

Let’s see how both the AR and MA models perform on the International-Airline-Passengers data.

AR model

AR_model = ARIMA(indexedDataset_logScale, order=(2,1,0)) AR_results = AR_model.fit(disp=-1) plt.plot(datasetLogDiffShifting) plt.plot(AR_results.fittedvalues, color='red') plt.title('RSS: %.4f'%sum((AR_results.fittedvalues - datasetLogDiffShifting['#Passengers'])**2))The RSS or sum of squares residual is 1.5023 in the case of the AR model, which is kind of dissatisfactory as AR doesn’t capture non-stationarity well enough.

MA Model

MA_model = ARIMA(indexedDataset_logScale, order=(0,1,2)) MA_results = MA_model.fit(disp=-1) plt.plot(datasetLogDiffShifting) plt.plot(MA_results.fittedvalues, color='red') plt.title('RSS: %.4f'%sum((MA_results.fittedvalues - datasetLogDiffShifting['#Passengers'])**2))The MA model shows similar results to AR, differing by a very small amount. We know our data is non-stationary, so let’s make this RSS score better by the non-stationarity handler AR+I+MA!

ARIMA

Along with the squashed use of the AR and MA model used earlier, ARIMA uses a special concept of Integration(I) with the purpose of differentiating some observations in order to make non-stationary data stationary, for better forecasting. So, it’s obviously better than its predecessor ARMA which could only handle stationary data.

What the differencing factor does is, that it takes into account the difference in predicted values between two timestamps (t and t+1, for example). Doing this helps in achieving a constant mean rather than a highly fluctuating ‘non-stationary’ mean.

Let’s fit the same data with ARIMA and see how well it performs!

ARIMA_model = ARIMA(indexedDataset_logScale, order=(2,1,2)) ARIMA_results = ARIMA_model.fit(disp=-1) plt.plot(datasetLogDiffShifting) plt.plot(ARIMA_results.fittedvalues, color='red') plt.title('RSS: %.4f'%sum((ARIMA_results.fittedvalues - datasetLogDiffShifting['#Passengers'])**2))Great! The graph itself speaks how ARIMA fits our data in a well and generalized fashion compared to the ARMA! Also, observe how the RSS has dropped to 1.0292 from 1.5023 or 1.4721.

SARIMAX

Designed and developed as a beautiful extension to the ARIMA, SARIMAX or, Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors is a better player than ARIMA in case of highly seasonal time series. There are 4 seasonal components that SARIMAX takes into account.

They are -

1. Seasonal Autoregressive Component

2. Seasonal Moving Average Component

3. Seasonal Integrity Order Component

4. Seasonal Periodicity

Source-Wikipedia

If you are more of a theory conscious person like me, do read more on this here, as getting into the details of the formula is beyond the scope of this article!

Now, let’s see how well SARIMAX performs on seasonal time-series data like the International-Airline-Passengers data.

from statsmodels.tsa.statespace.sarimax import SARIMAX SARIMAX_model=SARIMAX(train['#Passengers'],order=(1,1,1),seasonal_order=(1,0,0,12)) SARIMAX_results=SARIMAX_model.fit() preds=SARIMAX_results.predict(start,end,typ='levels').rename('SARIMAX Predictions') test['#Passengers'].plot(legend=True,figsize=(8,5)) preds.plot(legend=True)Look how beautifully SARIMAX handles seasonal time series!

Heading to DL Methods for Complex Time-Series ForecastingOne of the very common features of time-series data is the long-term dependency factor. It is obvious that many time-series forecasting works on previous records (the future is forecasted based on previous records, which may be far behind). Hence, ordinary traditional machine learning models like ARIMA, ARMA, or SARIMAX are not capable of capturing long-term dependencies, which makes them poor guys in sequence-dependent time series problems.

To address such an issue, a massively intelligent and robust neural network architecture was proposed which can extraordinarily handle sequence dependence. It was known as Recurrent Neural Networks or RNN.

Source-Medium

RNN was designed to work on sequential data like time series. However, a very remarkable pitfall of RNN was that it couldn’t handle long-term dependencies. For a problem where you want to forecast a time series based on a huge number of previous records, RNN forgets the maximum of the previous records which occurred much earlier, and only learns sequences of recent data fed to its neural network. So, RNN was observed to not be up to the mark for NSP (Next Sequence Prediction) tasks in NLP and time series.

To address this issue of not capturing long-term dependencies, a powerful variant of RNN was developed, known as LSTM (Long Short Term Memory) Networks. Unlike RNN, which could only capture short-term sequences/dependencies, LSTM, as its name suggests was observed to learn long as well as short term dependencies. Hence, it was a great success for modelling and forecasting time series data!

Note — Since explaining the architecture of LSTM will be beyond the size of this blog, I recommend you to head over to my article where I explained LSTM in detail!

Let us now take our Airline Passengers’ data and see how well RNN and LSTM work on it!

Imports —

import numpy as np import pandas as pd import tensorflow as tf import matplotlib.pyplot as plt import sklearn.preprocessing from sklearn.metrics import r2_score from keras.layers import Dense, Dropout, SimpleRNN, LSTM from keras.models import SequentialScaling the data to make it stationary for better forecasting —

minmax_scaler = sklearn.preprocessing.MinMaxScaler() data['Passengers'] = minmax_scaler.fit_transform(data['Passengers'].values.reshape(-1,1)) data.head()Scaled data —

Train, test splits (80–20 ratio) —

split = int(len(data[‘Passengers’])*0.8) x_train,y_train,x_test,y_test = np.array(x[:split]),np.array(y[:split]), np.array(x[split:]), np.array(y[split:]) #reshaping data to original shape x_train = np.reshape(x_train, (split, 20, 1)) x_test = np.reshape(x_test, (x_test.shape[0], 20, 1))RNN Model —

model = Sequential() model.add(SimpleRNN(40, activation="tanh", return_sequences=True, input_shape=(x_train.shape[1],1))) model.add(Dropout(0.15)) model.add(SimpleRNN(50, return_sequences=True, activation="tanh")) model.add(Dropout(0.1)) #remove overfitting model.add(SimpleRNN(10, activation="tanh")) model.add(Dense(1)) model.summary()Complie it, fit it and predict—

model.fit(x_train, y_train, epochs=15, batch_size=50) preds = model.predict(x_test)

Let me

Pretty much accurate!

LSTM Model —

model = Sequential() model.add(LSTM(100, activation="ReLU", return_sequences=True, input_shape=(x_train.shape[1], 1))) model.add(Dropout(0.2)) model.add(LSTM(80, activation="ReLU", return_sequences=True)) model.add(Dropout(0.2)) model.add(LSTM(50, activation="ReLU", return_sequences=True)) model.add(Dropout(0.2)) model.add(LSTM(30, activation="ReLU")) model.add(Dense(1)) model.summary()Complie it, fit it and predict—

model.fit(x_train, y_train, epochs=15, batch_size=50) preds = model.predict(x_test)Let me show you a picture of how well the model predicts —

Here, we can easily observe that RNN does the job better than LSTMs. As it is clearly seen that LSTM works great in training data but bad invalidation/test data, which shows a sign of overfitting!

Hence, try to use LSTM only where there is a need for long-term dependency learning otherwise RNN works good enough.

ConclusionCheers on reaching the end of the guide and learning pretty interesting kinds of stuff about Time Series. From this guide, you successfully learned the basics of time series, got a brief idea of the difference between Time Series Analysis and Forecasting subdomains of Time Series, a crisp mathematical intuition on Time Series analysis and forecasting techniques and explored how to work on Time Series problems in Machine Learning and Deep Learning to solve complex problems.

Hope you had fun exploring Time Series with Machine Learning and Deep Learning along with intuition! If you are a curious learner and want to “not” stop learning more, head over to this awesome notebook on time series provided by TensorFlow!

Feel free to follow me on Medium and GitHub for more articles and notebooks on Machine & Deep Learning! Connect with me on LinkedIn if you want to discuss anything regarding this article!

Happy Learning!

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Related

## Growth And Development Of An Organism

Introduction

One of the fundamental characteristics of living organisms is their ability to grow, i.e., to increase in size and/or cell number. Even monerans and protists undergo growth by multiplication. In higher organisms including plants and animals, growth is accompanied by development, which usually entails the evolution of certain special abilities and functions, and changes in morphological and physiological forms.

GrowthAny sort of irreversible increase in the size of an organism is referred to as growth. Growth is a result of an increment in the number of cells and enlargement of an individual cell.

Types of growth in plants

Primary growth − The division and elongation of the meristematic cells at the root and shoot apices, leading to increased root and shoot lengths.

Secondary growth − The division of the lateral meristems (i.e., the vascular cambium and cork cambium), leading to an increase in the width or thickness of some plants.

Characteristics of Growth

Growth is irreversible, contributing to the increasing complexity of an organism’s form and function

It includes an increase in the number of cells and the size of the cells

At the cellular level, growth involves an increase in the amount of protoplasm in cells

Growth may be determinate (i.e., may stop after some time), or indeterminate (i.e., growth continues throughout life)

Growth is measurable

DevelopmentDevelopment refers to the formation of a complex multicellular organism from a single cell. It entails differentiation of the zygote into different cell types, morphogenesis, development of functional, metabolic, and physiological capabilities, and environmental integration.

Stages of development in humans

Infancy − (from birth to 1 year old): The infant undergoes important developments and must be provided with ample nourishment by the mother

Childhood − (1 to 10 years): characterised by cognitive, physical, motor, and emotional developments.

Adolescence − (11 -17 years): marked by various transformations, including rapid physical, psychosocial and bio-behavioural developments. The most important development is that of puberty, i.e., attainment of sexual maturity

Adulthood − begins from 18 years of age, characterised by the completion of sexual maturity and cognitive development.

Middle age − (40-60 years). Generally characterised by declining body functioning and decreased physical strength, and an overall decline in the functioning of the CNS, eventually leading to old age.

Old age − (60 and above): aka senescence, the final stage in the lifetime of a human, characterised by the overall diminishing of an individual’s cognitive, emotional, sensory, perceptual, and physical abilities

Stages of development in plants

The vegetative stage − This stage involves the development of the plant from the embryo. The radicle and the plumule develop into the roots and the shoot respectively. Leaves grow and perform photosynthesis.

The reproductive stage − during this stage the plant develops its inflorescence, to receive the pollen during pollination. The reproductive stage ends with fertilization. and the eventual formation of a fruit with seeds inside it

Senescence − This stage is the final step in the development of a plant, marked by extreme changes in the leaves including degradation of chlorophyll and redistribution of nutrients.

Areas of Development Quantitative and Qualitative developmentQuantitative development refers to the changes in size and the number of cells in an organism. Qualitative development refers to the changes in the constitution and nature of an organism. For example, the growth of a neonate into an adult is accompanied by a plethora of developments in functional abilities and morphological characteristics.

Structural and Functional DevelopmentThe beginning of a single-celled zygote and the gradual but complex development into a fully functioning multicellular organism is a result of various kinds of structural and functional developments. Structural development involves the transformation of the cells of the body via the processes of cell commitment and differentiation.

Progressive and Regressive DevelopmentDevelopment is usually associated with increasing complexities in the body organisation and higher functional capabilities, known as progressive development. However, development can also be regressive, entailing the loss of certain functional body parts, or a size reduction. Progressive and regressive development often occur simultaneously during the growth of an organism.

Factors affecting Growth and Development

Heredity − An individual organism inherits the majority of its form and function from its parents. It not only influences the morphological characteristics but also the metabolic and functional capacities and health of an organism.

Hormones − These chemicals influence different areas of development in both plants, and animals. For example, the growth hormone in humans stimulates growth, the follicle-stimulating hormone and testosterone influence reproductive abilities, etc. In plants, hormones such as auxins, gibberellins, cytokinins and abscisic acid are essential for ensuring optimal growth and development.

Environment − An organism’s physical environment greatly influences its growth and functioning. Nutrients, water, temperature and climate conditions, atmospheric pressure, presence of pollutants and teratogens, etc affect the growth rate and course of development.

Laws of Growth and Development

Cephalocaudal principle − Growth and development occur along the top-bottom axis, i.e., from the head and downwards. The brain develops first, being the control centre of the body. As observed distinctly in foetuses of vertebrates, the head develops first and is very prominent, and eventually, the hand and leg buds are also formed. Moreover, an infant first learns to control its head, then gains control of its hands and eventually learns to crawl, stand and walk.

Proximodistal principle − Development occurs from the centre of the body in an outward manner. Hence, the spinal cord develops first, followed by the development of the arms, hands, and finally the fingers. Moreover, a child learns to control his shoulders and hands first and eventually learns to hold things with his fingers.

Development is a continuous phenomenon, from the birth to the death of an organism

Growth and development always occur sequentially. For example, a human always develops from the fetus through infancy, childhood, adolescence adulthood, and eventually reaches old age.

Conclusion

An increase in the size and the number of cells in an organism is termed growth. In plants, growth is of two types- primary and secondary

Development refers to the transformation of a single-celled zygote into a complex and fully functional organism. It involves quantitative, qualitative, structural, functional, progressive and regressive changes.

Growth and development are continuous and sequential and always occur from the top-bottom and from the proximal to distal axes of the body. They are affected by intrinsic factors, including heredity and hormones, and environmental factors

FAQsQ1. What happens when the growth hormone is under or over-secreted?

Q2. In which group of plants is secondary growth absent?

Ans. Herbaceous plants lack lateral meristems. Hence, secondary growth is absent in such plants.

Q3. What is the main difference between angiosperms and animal development?

Ans. Gastrulation and the haplodiplontic life cycle are characteristic of angiosperms development which does not occur in animals

Q4. What is cell commitment?

Ans. Cell commitment refers to the dedication to a particular specialised fate, it includes cell specification, cell determination and cell differentiation.

## Amazon Ads: Skyrocketing Growth In Q1

Amazon’s Role in the Q1 DeclineLike what we’ve seen with other Q1 platform analysis, Amazon’s pattern was similar: a strong Q1 that hit a wall right at the end.

However, unlike the other platforms, Amazon showed meteoric growth year over year, muscling its way to a seat at the table that’s predominantly owned by Google and Facebook.

Amazon announced a cutback on fulfillment of non-essential and third party fulfillment at the start of the pandemic. Commonly referred to as “FBA,” Fulfillment By Amazon acts as the warehouse and shipper for ecommerce brands that elect to use them for order fulfillment.

This created an interesting situation for sellers who were hoping to capitalize on the inevitable increase of online ordering – now they couldn’t get their items fulfilled.

While some categories were exempt if they were deemed “essential,” there was speculation about what this could mean for their overall ad revenue for Q1.

Ad Revenue Gains & LossesQ1 started off with major gains year-over-year for Amazon Ads, with 44% growth to $3.9b.

This collided with a reduction in conversion rates, an average decline of 10% as reported by Tinuiti.

All of this added up to cheaper ad rates, but in an environment where demand couldn’t be met by suppliers.

Merkle saw impressive gains year over year, something analysts are believing will continue as the gears of ecommerce start to turn more freely again. Year over year, Merkle saw growth in the following ways:

The Dichotomy of Demand vs. Ability to SupplyThe challenges faced by ecommerce sellers aren’t solely due to Amazon’s temporary fulfillment cutbacks. Most production of items takes place in China, the epicenter of the COVID-19 pandemic.

This rendered “business as usual” out the window, with reduced staffing and shelter-at-home mandates disrupting the labor force. As production rate slowed in China, this created a gap in fulfillment for sellers who typically rely on predictable system.

China has recovered and started to produce again, but then there was a new issue:

Coronavirus had moved to the United States, affecting everything from worker staffing in warehouses, to staffing at shipping docks.

Combine that with Amazon cutting back on fulfillment, and it’s been a challenging time for logistics with physical inventory.

## Top Robotic Companies That Received Funding In July 2023

Robotic technology will shape the world for better efficiency.

The Robotic Industry is changing the landscape of work in the modern era. Right from automation in every industry to autonomous surgeries in healthcare, Realtime Robotics is an autonomous industrial robotics company. The company offers real-time, collision-free motion planning that enables users to leverage robotic control technology to navigate applications. With just minimal programming, users can control the functioning of robots across multiple deployments. Realtime Robotics raised US$31.4 million in its Series A round. The funding was led by HAHN Automation for the purpose of improving robotic capabilities.

Verve Motion pioneers connected wearable technology for the industrial sector. It accompanies robotics into functional apparel and boosts worker safety and wellbeing with their technology. The company recently announced that it has raised US$15 million in Series A funding which was led by Construct Capital along with Founder Collective, Pillar VC, Safar Partners, OUP, and other angel investors.

Seoul Robotics is a 3D computer vision company that innovates intelligent robotic perception systems using artificial intelligence and machine learning. The company’s first commercial model, Discovery, made its debut in the US market, earlier this year. It is an all-in-one sensor and software platform that expands access, reduces costs, and simplifies the implementation of LiDAR-powered solutions in several applications for smart cities, smart, factories, and logistic mobility. Seoul Robotics was selected as an Innovative Icon startup for all its efforts and received a US$12 million investment from the Korean Government.

The Robotic Industry is changing the landscape of work in the modern era. Right from automation in every industry to autonomous surgeries in healthcare, robotics is now becoming capable of handling intricate responsibilities and repetitive tasks and perform them without errors. This is one of the reasons, industries are increasing their dependency on robotics . While this indicates the future of the industry, many organizations and startups are leveraging this demand to create innovative solutions. Here are the robotic companies that received funding in the month of July to carry on their work and research.Realtime Robotics is an autonomous industrial robotics company. The company offers real-time, collision-free motion planning that enables users to leverage robotic control technology to navigate applications. With just minimal programming, users can control the functioning of robots across multiple deployments. Realtime Robotics raised US$31.4 million in its Series A round. The funding was led by HAHN Automation for the purpose of improving robotic capabilities.Verve Motion pioneers connected wearable technology for the industrial sector. It accompanies robotics into functional apparel and boosts worker safety and wellbeing with their technology. The company recently announced that it has raised US$15 million in Series A funding which was led by Construct Capital along with Founder Collective, Pillar VC, Safar Partners, OUP, and other angel investors.Seoul Robotics is a 3D computer vision company that innovates intelligent robotic perception systems using artificial intelligence and machine learning. The company’s first commercial model, Discovery, made its debut in the US market, earlier this year. It is an all-in-one sensor and software platform that expands access, reduces costs, and simplifies the implementation of LiDAR-powered solutions in several applications for smart cities, smart, factories, and logistic mobility. Seoul Robotics was selected as an Innovative Icon startup for all its efforts and received a US$12 million investment from the Korean chúng tôi so much of an investment, but a business firm, Zebra Technologies is planning to acquire Fetch Robotics, a cloud-driven autonomous mobile robot startup. This acquisition aims to boost Zebra Technologies Enterprise Asset Intelligence vision and growth in industrial automation. This will align with Zebra Technology’s focus on robotics and change the infrastructure of the industry with seamless integration.

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